@inproceedings{MISTCelaya2024,
    author = {Celaya, A. and Lim, E. and Glenn, R. and Mi, B. and Balsells, A. and Netherton, T. and Chung, C. and Riviere, B. and Fuentes, D.},
    title = {{MIST: a simple and scalable end-to-end 3D medical imaging segmentation framework}},
    booktitle = {Medical Image Computing and Computer Assisted Intervention - MICCAI 2024},
    note={arXiv:2407.21343},
    year = {2024}
}

@article{CelayaKirkFuentesRiviere2024,
title={Solutions to elliptic and parabolic problems via finite difference based unsupervised small linear convolution neural networks},
author={Celaya, A. and Kirk, K. and Fuentes, D. and Riviere, B.},
journal={Computers and Mathematics with Applications},
year={2024},
pages={31--42},
volume={174},
Keywords={Scientific Machine Learning, Parabolic, Data Science}
}

@article{KirkRiviere2024,
title={A combined mixed hybrid and hybridizable discontinuous {G}alerkin method for {D}arcy flow and transport},
author={Kirk, K. and Riviere, B.},
journal={Journal of Scientific Computing},
volume={100},
number={2},
pages={57},
year={2024},
Keywords={Discontinuous Galerkin, Transport, Convection–Diffusion}
}

@article{MasriKuchtaRiviere,
title={Discontinuous Galerkin methods for 3D-1D systems},
author={R. Masri and M. Kuchta and B. Riviere},
journal={SIAM Journal on Numerical Analysis},
volume={62},
number={24},
pages={1814--1843},
year={2024},
Keywords={Discontinuous Galerkin, 3D-1D Coupling, Blood Flow, Mathematical Biology}
}

@article{LiuRiviereShenZhang,
title={A simple and efficient convex optimization based bound-preserving high order accurate limiter for {Cahn-Hilliard-Navier-Stokes} system},
author={Liu, Chen and Riviere, Beatrice and Shen, Jie and Zhang, Xiangxiong},
journal={SIAM Journal on Scientific Computing},
volume={46},
number={3},
pages={A1923--A1948},
year={2024},
Keywords={Discontinuous Galerkin, Diffuse Interface, Limiters}
}

@article{PoomPuelzRiviere2024,
title={Predicting the effects of surgically determined parameters on exercise tolerance in {F}ontan patients},
journal={Medical Engineering and Physics},
author={Kritpracha, P. and B. Riviere and C. Puelz},
year={2024},
Keywords={Blood Flow, Transport, Heart, Mathematical Biology}
}

@article{JoshaghaniRiviere2023,
title={Bound-preserving discontinuous Galerkin methods for compressible two-phase flows in porous media},
author={Joshaghani, M.S. and Riviere, B.},
journal={International Journal for Numerical Methods in Engineering},
volume={125},
number={4},
pages={e7396},
year={2024},
Keywords={Two-Phase Flow, Multiphase Flow, Discontinuous Galerkin, Limiters}
}

@article{KirkMasriRiviere2023,
title={Numerical analysis of a hybridized discontinuous {G}alerkin method for the {C}ahn-{H}illiard problem},
author={Kirk, K. and Masri, R. and Riviere, B.},
journal={IMA Journal of Numerical Analysis},
pages={drad075},
year={2023},
Keywords={Discontinuous Galerkin, Diffuse Interface}
}

@article{Celaya2023,
title={FMG-Net and W-Net: Multigrid Inspired Deep Learning Architectures For Medical Imaging Segmentation},
author={Celaya, A. and Riviere, B. and Fuentes, D.},
journal={Neurips 2023},
year={2023},
Keywords={Machine Learning, Image Segmentation, Mathematical Biology, Data Science}
}

@article{Celaya2022,
title={PocketNet: a smaller neural network for 3D medical image segmentation},
author={Celaya, A. and Actor, J. and Muthosivarajan, R. and Gates, E. and Chung, C. and Schellingerhout, D. and Riviere, B. and Fuentes, D.},
journal={IEEE Transactions on Medical Imaging},
volume={42},
number={4},
pages={1172--1184},
year={2023},
doi={10.1109/TMI.2022.3224873},
Keywords={Machine Learning, Image Segmentation, Mathematical Biology, Data Science}
}

@article{MasriShenRiviere,
title={Discontinuous Galerkin Approximations to elliptic and parabolic problems with a Dirac line source},
author={Masri, R. and Shen, B. and Riviere, B.},
journal={ESAIM: Mathematical Modelling and Numerical Analysis},
volume={57},
pages={585--620},
year={2023},
doi={10.1051/m2an/2022095},
Keywords={Diffusion, Discontinuous Galerkin}
}

@article{MasriLiuRiviere2023,
title={Improved a priori error estimates for a discontinuous Galerkin pressure correction scheme for the Navier-Stokes equations},
author={Masri, R. and Liu, C. and Riviere, B.},
journal={Numerical Methods for Partial Differential Equations}, 
year={2023},
pages={3108--3144},
volume={39},
Keywords={Navier-Stokes, Discontinuous Galerkin}
}

@article{LiuMasriRiviereSINUM,
title={Convergence of a decoupled splitting scheme for the Cahn--Hilliard--Navier--Stokes system},
author={Liu, C. and Masri, R. and Riviere, B.},
journal={SIAM Journal on Numerical Analysis},
volume={61},
number={6},
pages={2651--2694},
year={2023},
Keywords={Pore-Scale, Diffuse Interface, Two-Phase Flow, Navier-Stokes, Discontinuous Galerkin}
}

@article{SosaJonesCappaneraRiviere,
title={Existence and convergence of a discontinuous Galerkin method for the incompressible three-phase flow problem in porous media},
author={Sosa Jones, G. and Riviere, B. and Cappanera, L.},
journal={IMA Journal of Numerical Analysis},
year={2022},
Keywords={Three-Phase Flow, Multiphase Flow, Discontinuous Galerkin}
}

@article{ShenRiviere,
title={A sequential discontinuous Galerkin method for two-phase flow in deformable porous media},
author={Shen, B. and Riviere, B.},
journal={Computer Methods in Applied Mechanics and Engineering},
volume={399},
pages={115266},
year={2022},
Keywords={Two-Phase Flow, Poroelasticity, Coupled Flow and Geomechanics}
}

@article{MasriLiuRiviereMathComp,
title={A discontinuous Galerkin pressure correction scheme for the incompressible Navier-Stokes equations: stability and convergence},
author={Masri, R. and Liu, C. and Riviere, B.},
journal={Mathematics of Computation},
volume={91},
pages={1625--1654},
year={2022},
Keywords={Navier-Stokes, Discontinuous Galerkin}
}

@article{JoshaghaniRiviereSekachev,
title={Maximum-principle-satisfying discontinuous Galerkin methods for incompressible two-phase immiscible flow},
author={Joshaghani, M.S. and Riviere, B. and M. Sekachev},
journal={Computer Methods in Applied Mechanics and Engineering},
volume={391},
pages={114550},
year={2022},
Keywords={Two-Phase Flow, Multiphase Flow, Discontinuous Galerkin, Limiters}
}

@article{JoshaghaniGiraultRiviere,
title={A vertex scheme for two-phase flow in heterogeneous media},
author={Joshaghani, M.S. and Girault, V. and Riviere, B.},
journal={Journal of Computational Physics},
volume={449},
year={2022},
Keywords={Two-Phase Flow, Multiphase Flow, Finite Element}
}

@article{LiuRayThieleLinRiviere,
title={A pressure-correction and bound-preserving discretization of the phase-field method for variable density two-phase flows},
author={Liu, Chen and Ray, Deep and Thiele, Christopher and Lin, Lu and Riviere, Beatrice},
journal={Journal of Computational Physics},
volume={449},
pages={110769},
year={2022},
Keywords={Discontinuous Galerkin, Pore-Scale, Diffuse Interface, Multiphase Flow, Two-Phase Flow}
}

@article{ThieleRiviere,
title={p-Multigrid with partial smoothing: an efficient preconditioner for discontinuous Galerkin discretizations with modal bases},
author={Thiele, Christopher and Riviere, Beatrice},
journal={Journal of Computational and Applied Mathematics},
volume={402},
pages={114815},
year={2022},
Keywords={Discontinuous Galerkin, Multigrid Methods, Solvers}
}

@Article{MasriPuelzRiviere2021,
title={A Discontinuous Galerkin Method for Blood Flow and Solute Transport in One Dimensional Vessel Networks},
author={R. Masri and C. Puelz and B. Riviere},
journal={Communications on Applied Mathematics and Computation},
volume={4},
number={2},
pages={500--529},
year={2022},

Keywords={Mathematical Biology, Blood Flow, Convection-Diffusion, Discontinuous Galerkin, Transport}
}

@article{BorceaRiviereWang,
title={Nonoverlapping domain decomposition method with preconditioner from asymptotic analysis of steady flow in high contrast media},
author={Borcea, L. and Riviere, B. and Wang, Y.},
journal={International Journal of Computer Mathematics},
volume={98},
number={10},
year={2021},
Keywords={Diffusion, Finite Volume, Single-Phase Flow}
}

@article{RayLiuRiviere,
title={A Discontinuous {G}alerkin method for a diffuse-interface model of immiscible two-phase flows with soluble surfactant},
author={Ray, Deep and Liu, Chen and Riviere, Beatrice},
journal={Computational Geosciences},
volume={25},
pages={1775-1792},
year={2021},
Keywords={Discontinuous Galerkin, Pore-Scale, Diffuse Interface, Multiphase Flow, Two-Phase Flow}
}

@article{GiraultRiviereCappaneraI,
title={A finite element method for degenerate two-phase flow in porous media. Part I: Well-posedness},
author={V. Girault and B. Riviere and L. Cappanera},
Journal= {Journal of Numerical Mathematics},
year={2021},
volume={29},
number={2},
pages={81--101},
Doi={10.1515/jnma-2020-0004},
Keywords = {Two-Phase Flow, Three-Phase Flow, Multiphase Flow, Finite Element}
}

@article{GiraultRiviereCappaneraII,
title={A finite element method for degenerate two-phase flow in porous media. Part II: Convergence},
author={V. Girault and B. Riviere and L. Cappanera},
Journal= {Journal of Numerical Mathematics},
year={2021},
volume={29},
number={3},
pages={187--219},
Doi={10.1515/jnma-2020-0005},
Keywords = {Two-Phase Flow, Three-Phase Flow, Multiphase Flow, Finite Element}
}

@Article{MasriPuelzRiviere2021b,
title={A Reduced Model for Solute Transport in Compliant Blood Vessels with Arbitrary Axial Velocity Profile},
author={R. Masri and C. Puelz and B. Riviere},
journal={International Journal of Heat and Mass Transfer},
year={2021},
Keywords={Mathematical Biology, Blood Flow, Transport}
}

@Article{HendryxRusinRiviere2021,
title={An Extended {DEIM} Algorithm for Subset Selection and Class Identification},
author={E. Hendryx and C. Rusin and B. Riviere},
journal={Journal of Machine Learning},
volume={110},
pages={621--650},
year={2021},
Doi={10.1007/s10994-021-0594-3},
Keywords={Data Analytics, Data Science}
}

@article{DoyleRiviereSekachev2020,
title={A multinumerics scheme for incompressible two-phase flow},
author={Doyle, Bryan and Riviere, Beatrice and Sekachev, Michael},
journal={Computer Methods in Applied Mechanics and Engineering},
volume={370},
year={2020},
Keywords = {Two-Phase Flow, Multiphase Flow, Discontinuous Galerkin, Finite Volume}
}

@article{Fuentes2020,
title={Mathematical modeling of mass and energy transport for thermoembolization},
author={D. Fuentes and S. Fahrenholtz and C. Guo and C. MackLellan and R. Layman and B. Riviere and J. Stafford and E. Cressman},
journal={International Journal of Hyperthermia},
volume={37},
number={1},
pages={356--365},
year={2020},
Keywords={Mathematical Biology, Multiphase Flow}
}

@article{FuentesThompson2020,
title={Imaging-based characterization of convective tissue properties},
author={D. Fuentes and E. Thompson and M. Jacobsen and A. Colleen Crouch and R.R. Layman and B. Riviere and E. Cressman},
journal={International Journal of Hyperthermia},
volume={27},
pages={155--163},
year={2020},
Keywords={Mathematical Biology}
}

@article{NedaRiviere,
title={A Discontinuous Galerkin Method for the Stolz-Adams Approximate Deconvolution Model for Turbulent Flows},
author={M. Neda and B. Riviere},
journal={Results in Applied Mathematics},
volume={8},
year={2020},
Keywords={Navier-Stokes, Turbulence}
}

@article{Liu2020,
title={Numerical Analysis of a Discontinuous Galerkin Method for Cahn-Hilliard-Navier-Stokes Equations},
author={C. Liu and B. Riviere},
journal={CSIAM Transactions on Applied Mathematics},
year={2020},
volume={1},
number={1},
pages={104--141},
keywords ={Pore-Scale, Diffuse Interface, Two-Phase Flow, Discontinuous Galerkin, Navier-Stokes}
}

@article{Liu2019a,
title={An Efficient Numerical Algorithm for Solving Viscosity Contrast Cahn-Hilliard-Navier-Stokes System in Porous Media},
author={C. Liu and F. Frank and C. Thiele and F.O. Alpak and S. Berg and W. Chapman and B. Riviere},
journal={Journal of Computational Physics},
year={2020},
number={400},
pages={108948},
keywords ={Pore-Scale, Diffuse Interface, Two-Phase Flow, Discontinuous Galerkin, Navier-Stokes}
}

@article{Actor,
title={Identification of Kernels in a Convolutional Neural Network:
Connections Between Level Set Equation and Deep Learning for Image Segmentation},
author={J. Actor, D. Fuentes and B. Riviere},
journal={Proc. SPIE Medical Imaging 2020: Image Processing},
volume={1131317},
OPTpages={},
year={2020},
Doi={10.1117/12.2548871},
Keywords={Machine Learning, Image Segmentation, Mathematical Biology, Data Science}
}

@article{FabienKnepleyRiviere2020bis,
title={Families of Interior Penalty Hybridizable discontinuous Galerkin methods for second order elliptic problems},
author={M. Fabien and M. Knepley and B. Riviere},
journal={Journal of Numerical Mathematics},
volume={28},
number={3},
year={2020},
Doi={10.1515/jnma-2019-0027},
Keywords={Diffusion, Discontinuous Galerkin}
}

@article{FabienKnepleyRiviere2020,
title={A high order hybridizable discontinuous Galerkin method for incompressible miscible displacement in heterogeneous media},
author={M. Fabien and M. Knepley and B. Riviere},
journal={Results in Applied Mathematics},
volume={8},
OPTpages={},
year={2020},
Keywords={Miscible Displacement, Discontinuous Galerkin}
}

@article{LiuFrankAlpakRiviere2019,
  title={An interior penalty discontinuous {G}alerkin approach for {3D} incompressible {N}avier--{S}tokes equation for permeability estimation of porous media},
  author={Liu, Chen and Frank, Florian and Alpak, Faruk O and Riviere, Beatrice},
  journal={Journal of Computational Physics},
  volume={396},
  pages={669--686},
  year={2019},
  keywords={Navier-Stokes, Pore-Scale}
}

@article{Thompson2018,
title={An implicit discontinuous Galerkin method for modeling acute edema and resuscitation in the small intestine},
author={T. Thompson and M. Knepley and B. Riviere},
journal={Mathematical Medicine \& Biology},
year={2019},
pages={513-548},
volume={36},
number={4},
Keywords={Poroelasticity,Mathematical Biology, Intestinal Edema}
}

@article{CappaneraRiviere,
title={A numerical method for solving the three-phase three-component  problem},
author={L. Cappanera and B. Riviere},
Journal= {Numerical Methods for Partial Differential Equations},
year={2019},
volume={35},
number={2},
pages={761--789},
notes={DOI 10.1002/num.22324},
Keywords = {Black-Oil, Three-Phase Flow, Multiphase Flow, Discontinuous Galerkin}
}

@article{LiuFrankRiviere,
title={Numerical Error Analysis For The Cahn-Hilliard Equation With General Chemical Energy Density},
author={C. Liu and F. Frank and B. Riviere},
journal={Numerical Methods for Partial Differential Equations},
volume={35},
number={4},
year={2019},
pages={1509-1537},
Keywords={Two-Phase Flow, Pore-Scale, Diffuse Interface}
}

@article{FabienKnepleyRiviere,
title={Manycore Parallel Computing For A Hybridizable Discontinuous Galerkin Nested Multigrid Method},
author={M. Fabien and M. Knepley and R. Mills and B. Riviere},
journal={SIAM Journal on Scientific Computing},
pages={C73-C96},
volume={41},
number={2},
year={2019},
Keywords={Solvers, Diffusion, Discontinuous Galerkin}
}


%%%%%%
% published or to appear
%%%%%%%%%

@inProceedings{ThieleArayaPoloAlpakRiviere2019,
title={Distributed Parallel Hybrid CPU-GPGPU Implementation of the Phase-Field Method for Accelerated High-Accuracy Simulations of Pore-Scale Two-Phase Flow},
Author={C. Thiele and M. Araya-Polo and F.O. Alpak and B. Riviere},
booktitle={SPE Reservoir Symposium},
publisher={Society for Petroleum Engineers},
year={2019},
number={SPE-193922-MS},

Keywords={Solvers, Diffuse Interface}
}

@inProceedings{CappaneraRiviereSPE,
title={Flexible Discretizations Of The Three-Component Three-Phase Flow Problem},
Author={L. Cappanera and B. Riviere},
booktitle={SPE Reservoir Symposium},
publisher={Society for Petroleum Engineers},
year={2019},
number={SPE-193906-MS},
Keywords = {Black-Oil, Three-Phase Flow, Multiphase Flow, Discontinuous Galerkin}
}

@inProceedings{DoyleRiviere,
title={Numerical Error Quantification Of Agent-Based Models As Applied To Oil Reservoir Simulation},
Author={B. Doyle and B. Riviere},
booktitle={SPE Reservoir Symposium},
publisher={Society for Petroleum Engineers},
year={2019},
number={SPE-193935-MS},

Keywords    = {Single-Phase Flow, Agent-Based Modeling}
}

@InProceedings{RiviereYang,
title={A DG Method for the simulation of  CO2 storage  in saline aquifer},
author={Riviere, Beatrice and Yang, Xin},
booktitle={Advances in the Mathematical Sciences - Research from the 2017 Association for Women in Mathematics Symposium},
year={2018},
volume={15},
pages={205-232},
Keywords={CO2 Storage, Two-Phase Flow, Multiphase Flow, Discontinuous Galerkin}
}

@article{ChaabaneRSC2018,
title={A parallelizable sequential method for the Biot system},
author={N. Chaabane and B. Riviere and M. Sekachev and H. Calandra},
journal={Journal of Numerical Analysis, Industrial and Applied Mathematics},
volume={12},
pages={21-34},
year={2018},
Keywords={Poroelasticity, Coupled Flow and Geomechanics}
}

@article{KanschatRiviereJSC,
title={A finite element method with strong mass conservation for {B}iot's linear consolidation model},
author={G. Kanschat and B. Riviere},
journal={Journal of Scientific Computing},
year={2018},
pages={1762--1779},
volume={77},
number={3},
notes={DOI: 10.1007/s10915-018-0843-2},
Keywords={Poroelasticity, Coupled Flow and Geomechanics, Finite Element}
}

@article{ChaabaneGiraultRiviereThompson,
title={A  Stable Enriched Galerkin Element for the Stokes Problem},
author={N. Chaabane and V. Girault and B. Riviere and T. Thompson},
journal={Applied Numerical Mathematics},
volume={132},
pages={1--21},
year={2018},
Keywords={Enriched Galerkin, Stokes, Navier-Stokes}
}

@article{MuFrankRiviereAlpakChapman,
title={Mass-Conserved Density Gradient Theory Model for Nucleation Process},
author={X. Mu and F. Frank and B. Riviere and F.O. Alpak and W. Chapman},
journal={Industrial and Engineering Chemistry Research},
year={2018},
pages={16476--16485},
volume={57},
number={48},
keywords ={Density Gradient Theory}
}

@article{FrankLiuSPE,
title={Direct Numerical Simulation of Flow on Pore-Scale Images Using the Phase-Field Method},
author={F. Frank and C. Liu and F.O. Alpak and S. Berg and B. Riviere},
journal={SPE Journal},
year={2018},
number={SPE-182607-PA},
note={October},
keywords ={Pore-Scale, Diffuse Interface, Two-Phase Flow, Discontinuous Galerkin}
}

@article{FrankLiuAlpakRiviere2017b,
title={An energy-based equilibrium contact angle boundary condition on jagged surfaces for phase-field methods},
author={F. Frank and C. Liu and A. Scanziani and O. Alpak and B. Riviere},
journal={Journal of Colloid \& Interface Science},
volume={523},
pages={282--291},
year={2018},
Doi={10.1016/j.jcis.2018.02.075},
Keywords                 = {Pore-Scale, Diffuse Interface, Two-Phase Flow, Multiphase Flow}
}

@article{FabienKnepleyRiviere2,
title={A hybridizable discontinuous Galerkin method for two-phase flow in heterogeneous porous media},
author={M. Fabien and M. Knepley and B. Riviere},
journal={International Journal for Numerical Methods in Engineering},
volume={116},
pages={161-177},
Doi={10.1002/nme.5919},
year={2018},
Keywords={Two-Phase Flow, Multiphase Flow, Discontinuous Galerkin}
}

 

@article{FrankLiuAlpakRiviere2017,
title={A finite volume/discontinuous Galerkin method for the advective {C}ahn-{H}illiard equation with degenerate mobility on porous domains stemming from micro-{CT} imaging},
author={F. Frank and C. Liu and O. Alpak and B. Riviere},
journal={Computational Geosciences},
volume={22},
number={2},
pages={543--563},
year={2018},
Doi={10.1007/s10596-017-9709-1},
Keywords  = {Pore-Scale, Diffuse Interface, Two-Phase Flow, Multiphase Flow, Discontinuous Galerkin, Finite Volume}
}

@Article{HendryxRiviereSorensenRusin,
title={Finding Representative Electrocardiogram Beat Morphologies with {CUR}},
author={E. Hendryx and B. Riviere and D. Sorensen and C. Rusin},
journal={Journal of Biomedical Informatics},
volume={77},
pages={97--110},
year={2018},
Doi={10.1016/j.jbi.2017.12.003},
Keywords={Data Analytics, Mathematical Biology, Data Science}
}

@Article{ChaabaneRiviere2017b,
Title={A splitting-based finite element method for the {B}iot poroelasticity system},
Author={N. Chaabane and B. Riviere},
Journal={Computers and Mathematics with Applications},
volume={75},
number={7},
pages={2328-2337},
year={2018},
Keywords={Poroelasticity, Coupled Flow and Geomechanics, Finite Element}
}

@article{PuelzAcosta2017,
title={A computational study of the {F}ontan circulation with fenestration or hepatic vein exclusion},
author={C. Puelz and S. Acosta and B. Riviere and D.J. Penny and K.M. Brady and C.G. Rusin},
journal={Computers in Biology and Medicine},
volume={89},
pages={405-418},
year={2017},
Keywords={Blood Flow, Heart, Mathematical Biology}
}

@article{AcostaPuelzRiviere2017,
title={Cardiovascular mechanics in the early stages of pulmonary hypertension: a computational study},
author={S. Acosta and C. Puelz and B. Riviere and D.J. Penny and K.M. Brady and C.G. Rusin},
journal={Biomechanics and Modeling in Mechanobiology},
volume={16},
number={6},
pages={2093--2112},
year={2017},
Keywords={Blood Flow, Heart, Mathematical Biology}
}

@article{ThieleEtAl2017IHSS,
title = {Inexact hierarchical scale separation: a two-scale approach for linear systems from discontinuous {G}alerkin discretizations},
author = {C. Thiele and M. Araya-Polo and F.O. Alpak and B. Riviere and F. Frank},
url = {https://github.com/lephlaux/ihss},
pages={1769--1778},
volume={74},
number={8},
year = {2017},
journal = {Computers and Mathematics with Applications},
Keywords={Solvers, Discontinuous Galerkin}
}

@Article{PuelzRiviere2017,
Title={A priori error estimates of {A}dams-{B}ashforth discontinuous {G}alerkin methods for scalar nonlinear conservation laws},
Author={C. Puelz and B. Riviere},
Journal={Journal of Numerical Mathematics},
volume={26},
number={3},
pages={151--172},
year = {2017},
Keywords={Hyperbolic, Blood Flow, Discontinuous Galerkin}
}

@Article{ChaabaneRiviere2017,
Title={A sequential discontinuous Galerkin method for the coupling of flow and geomechanics},
Author={N. Chaabane and B. Riviere},
Journal={Journal of Scientific Computing},
volume={74},
number={1},
pages={375-395},
year={2017},
Keywords={Poroelasticity, Coupled Flow and Geomechanics, Discontinuous Galerkin}
}

@Article{ChaabaneGiraultPuelzRiviere2017,
Title = {Convergence of {IPDG} for coupled time-dependent {Navier-Stokes and Darcy} equations},
Author = {N. Chaabane and V. Girault and C. Puelz and B. Riviere},
Journal = {Journal of Computational and Applied Mathematics},
volume={324},
pages={25--48},
year = {2017},
Keywords = {Coupled Surface and Subsurface, Discontinuous Galerkin, Navier-Stokes}
}

@Article{RiviereTanThompson2017,
 Title	= {Error analysis of primal discontinuous Galerkin methods for a mixed formulation of the Biot equations},
 Author = {B. Riviere and J. Tan and T. Thompson},
 Journal = {Computers and Mathematics with Applications},
 volume = {73},
 pages = {666--683},
 Year = {2017},
 Doi = {10.1016/j.camwa.2016.12.030},
 Keywords = {Poroelasticity, Coupled Flow and Geomechanics, Discontinuous Galerkin}
}

@Article{PuelzCanicRiviereRusin2017,
  Title                    = {Comparison of reduced models for blood flow using {R}unge-{K}utta discontinuous {G}alerkin methods},
  Author                   = {C. Puelz and S. Canic and B. Riviere and C. Rusin},
  Journal                  = {Applied Numerical Mathematics},
  Year                     = {2017},
  Pages                    = {114--141},
  Volume                   = {115},
  Keywords                 = {Blood Flow, Hyperbolic, Mathematical Biology, Discontinuous Galerkin}
}

@Article{GiraultLiRiviereNMPDE,
  Title                    = {Strong convergence of the discontinuous Galerkin scheme for the low regularity miscible displacement equations},
  Author                   = {V. Girault and J. Li and B. Riviere},
  Journal                  = {Numerical Methods for Partial Differential Equations},
  Year                     = {2017},
  Number                   = {2},
  Pages                    = {489–513},
  Volume                   = {33},
  Keywords                 = {Miscible Displacement, Discontinuous Galerkin}
}

@InProceedings{FrankLiuAlpakPoloRiviere2017,
Title={A discontinuous Galerkin finite element framework for the direct numerical simulation of flow on high-resolution pore-scale images},
Author={Frank, F. and Liu, C. and Alpak, F. and Araya-Polo, M. and Riviere, B.},
booktitle={SPE Reservoir Symposium},
publisher={Society for Petroleum Engineers},
year={2017},
number={SPE-182606-MS},
Keywords = {Pore-Scale, Diffuse Interface, Multiphase Flow}
}

@InProceedings{ThielePoloAlpakRiviereFrank2017,
Title={Inexact hierarchical scale separation: an efficient linear solver for discontinuous Galerkin discretizations},
Author={Thiele, C. and Araya-Polo, M. and Alpak, F.  and Riviere, B. and Frank, F.},
booktitle={SPE Reservoir Symposium},
publisher={Society for Petroleum Engineers},
year={2017},
number={SPE-182671-MS},
Keywords = {Solvers, Diffuse Interface}
}

@Article{AlpakRiviereFrank2016,
  Title                    = {A phase-field method for the direct simulation of two-phase flows in pore-scale media using a non-equilibrium wetting boundary condition},
  Author                   = {Alpak, Faruk O. and Riviere, Beatrice and Frank, Florian},
  Journal                  = {Computational Geosciences},
  Year                     = {2016},
  Pages                    = {1–28},

  Abstract                 = {Advances in pore-scale imaging (e.g., $\mu$-CT scanning), increasing availability of computational resources, and recent developments in numerical algorithms have started rendering direct pore-scale numerical simulations of multi-phase flow on pore structures feasible. Quasi-static methods, where the viscous and the capillary limit are iterated sequentially, fall short in rigorously capturing crucial flow phenomena at the pore scale. Direct simulation techniques are needed that account for the full coupling between capillary and viscous flow phenomena. Consequently, there is a strong demand for robust and effective numerical methods that can deliver high-accuracy, high-resolution solutions of pore-scale flow in a computationally efficient manner. Direct simulations of pore-scale flow on imaged volumes can yield important insights about physical phenomena taking place during multi-phase, multi-component displacements. Such simulations can be utili
 zed for optimizing various enhanced oil recovery (EOR) schemes and permit the computation of effective properties for Darcy-scale multi-phase flows.},
  Doi                      = {10.1007/s10596-015-9551-2},
  Keywords                 = {Pore-Scale, Diffuse Interface, Two-Phase Flow, Multiphase Flow}
}

Advances in pore-scale imaging (e.g., $μ$-CT scanning), increasing availability of computational resources, and recent developments in numerical algorithms have started rendering direct pore-scale numerical simulations of multi-phase flow on pore structures feasible. Quasi-static methods, where the viscous and the capillary limit are iterated sequentially, fall short in rigorously capturing crucial flow phenomena at the pore scale. Direct simulation techniques are needed that account for the full coupling between capillary and viscous flow phenomena. Consequently, there is a strong demand for robust and effective numerical methods that can deliver high-accuracy, high-resolution solutions of pore-scale flow in a computationally efficient manner. Direct simulations of pore-scale flow on imaged volumes can yield important insights about physical phenomena taking place during multi-phase, multi-component displacements. Such simulations can be utili zed for optimizing various enhanced oil recovery (EOR) schemes and permit the computation of effective properties for Darcy-scale multi-phase flows.

@Article{DongRiviere2016,
  Title                    = {A semi-implicit method for incompressible three-phase flow in porous media},
  Author                   = {J. Dong and B. Riviere},
  Journal                  = {Computational Geosciences},
  Year={2016},
  Volume={20},
  Pages={1169--1184},
  OPTNote={DOI 10.1007/s10596-016-9583-2},
  Keywords                 = {Three-Phase Flow, Multiphase Flow, Discontinuous Galerkin}
}

@Article{GiraultLiRiviere2016,
  Title                    = {Strong convergence of discrete DG solutions of the heat equation},
  Author                   = {V. Girault and J. Li and B. Riviere},
  Journal                  = {Journal of Numerical Mathematics},
  volume={24},
  number={4},
  pages={235--252},
  year={2016},
  Keywords		   = {Diffusion, Parabolic, Discontinuous Galerkin}
}

@Article{LiRiviere2016Fingering,
  Title                    = {Numerical modeling of miscible viscous fingering instabilities by high-order methods},
  Author                   = {Li, Jizhou and Riviere, Beatrice},
  Journal                  = {Transport in Porous Media},
  Year                     = {2016},
  Number                   = {3},
  Pages                    = {607–628},
  Volume                   = {113},
  note			   = {DOI 10.1007/s11242-016-0715-x},
  Keywords		   = {Miscible Displacement, Discontinuous Galerkin},

  Abstract                 = {In this paper, a high-order method is used to simulate the viscous fingering fluid instability during the miscible displacement process in porous media, on structured and unstructured grids. The numerical model incorporates decoupling in time, discontinuous Galerkin method of high order, flux reconstruction and parallel implicit solvers to produce an accurate and efficient predictive tool for finger growth. This paper shows that the proposed numerical approach is a competitive method to simulate several viscous fingering problems, such as rectilinear flow, density-driven flow and radial flow. The numerical model does not suffer from grid orientation, and accurately measures finger growth rate. Convergence of the fingering pattern is obtained under mesh refinement and increased polynomial degree.},
  Doi                      = {10.1007/s11242-016-0715-x},
  ISSN                     = {1573-1634},
  Url                      = {http://dx.doi.org/10.1007/s11242-016-0715-x}
}

In this paper, a high-order method is used to simulate the viscous fingering fluid instability during the miscible displacement process in porous media, on structured and unstructured grids. The numerical model incorporates decoupling in time, discontinuous Galerkin method of high order, flux reconstruction and parallel implicit solvers to produce an accurate and efficient predictive tool for finger growth. This paper shows that the proposed numerical approach is a competitive method to simulate several viscous fingering problems, such as rectilinear flow, density-driven flow and radial flow. The numerical model does not suffer from grid orientation, and accurately measures finger growth rate. Convergence of the fingering pattern is obtained under mesh refinement and increased polynomial degree.

@Article{AcostaPuelzRivierePennyRusin2015,
  Title                    = {Numerical method of characteristics for one-dimensional blood flow},
  Author                   = {S. Acosta and C. Puelz and B. Riviere and D. Penny and C. Rusin},
  Journal                  = {Journal of Computational Physics},
  Year                     = {2015},
  Pages                    = {96–109},
  Volume                   = {294},
  Doi			   = {10.1016/j.jcp.2015.03.045},

  Keywords                 = {Blood Flow, Hyperbolic, Mathematical Biology, Method of Characteristics}
}

@Article{LiRiviere2015-cmame,
  Title                    = {Numerical solutions of the incompressible miscible displacement equations in heterogeneous media},
  Author                   = {Li, Jizhou and Riviere, Beatrice},
  Journal                  = {Computer Methods in Applied Mechanics and Engineering},
  Year                     = {2015},
  Pages                    = {107–121},
  Volume                   = {292},
  Doi			   = {10.1016/j.cma.2014.10.048},

  Keywords                 = {Miscible Displacement, Discontinuous Galerkin},
  Publisher                = {Elsevier}
}

@Article{LiRiviere2015-compgeo,
  Title                    = {High order discontinuous Galerkin method for simulating miscible flooding in porous media},
  Author                   = {J. Li and B. Riviere},
  Journal                  = {Computational Geosciences},
  Year                     = {2015},
  Number                   = {6},
  Pages                    = {1251–1268},
  Volume                   = {19},
  note			   = {DOI 10.1007/s10596-015-9541-4},

  Keywords                 = {Miscible Displacement}
}

@Article{LiRiviereWalkington2015,
  Title                    = {Convergence of a high order method in time and space for the miscible displacement equations},
  Author                   = {Li, Jizhou and Riviere, Beatrice and Walkington, Noel},
  Journal                  = {ESAIM: Mathematical Modelling and Numerical Analysis},
  Year                     = {2015},
  Pages                    = {953–976},
  Volume                   = {49},
  note			   = {DOI: 10.1051/m2an/2014059},

  Keywords                 = {Miscible Displacement}
}

@Article{RankinRiviere2015,
  Title                    = {A high order method for solving the black-oil problem in porous media},
  Author                   = {R. Rankin and B. Riviere},
  Journal                  = {Advances in Water Resources},
  Year                     = {2015},
  Pages                    = {126–144},
  Volume                   = {78},

  Keywords                 = {Black-Oil, Three-Phase Flow, Multiphase Flow}
}

@Article{YoungOsizikRiviereShamim2015,
  Title                    = {A comprehensive mathematical framework for modeling intestinal smooth muscle cell contraction with applications to intestinal edema},
  Author                   = {J. Young and S. Ozisik and B. Riviere and M. Shamim},
  Journal                  = {Mathematical Biosciences},
  Year                     = {2015},
  Pages                    = {206–213},
  Volume                   = {262},
  Doi			   = {10.1016/j.mbs.2014.12.009},

  Keywords                 = {Intestinal Edema, Mathematical Biology}
}

@Article{GiraultKanschatRiviere2014,
  Title                    = {Error analysis for a monolithic discretization of coupled Darcy and Stokes problems},
  Author                   = {Girault, Vivette and Kanschat, Guido and Riviere, Beatrice},
  Journal                  = {Journal of Numerical Mathematics},
  Year                     = {2014},
  Number                   = {2},
  Pages                    = {109–142},
  Volume                   = {22},

  Keywords                 = {Coupled Surface and Subsurface}
}

@Article{RiviereSardar2014,
  Title                    = {Penalty-free discontinuous Galerkin methods for incompressible Navier–Stokes equations},
  Author                   = {B. Riviere and S. Sardar},
  Journal                  = {Mathematical Models and Methods in Applied Sciences},
  Year                     = {2014},
  Number                   = {6},
  Pages                    = {1217–1236},
  Volume                   = {24},
  Keywords                 = {Navier–Stokes}
}

@Article{RiviereYang2014,
  Title                    = {Convergence analysis of a coupled method for time-dependent convection–diffusion equations},
  Author                   = {B. Riviere and X. Yang},
  Journal                  = {Numerical Methods for Partial Differential Equations},
  Year                     = {2014},
  Number                   = {1},
  Pages                    = {133–157},
  Volume                   = {30},

  Keywords                 = {Transport, Convection–Diffusion, Finite Volume}
}

@Article{YoungRiviereUrayCox2014,
  Title                    = {A mathematical model of intestinal oedema formation},
  Author                   = {Young, J. and Riviere, B. and Uray, K. and Cox, C.},
  Journal                  = {Mathematical Medicine \& Biology},
  Year                     = {2014},
  Number                   = {1},
  Pages                    = {1–15},
  Volume                   = {31},

  Keywords                 = {Intestinal Edema, Mathematical Biology}
}

@Article{CesmeliogluGiraultRiviere2013,
  Title                    = {Time-dependent coupling of Navier–Stokes and Darcy flows},
  Author                   = {A. Cesmelioglu and V. Girault and B. Riviere},
  Journal                  = {ESAIM: Mathematical Modelling and Numerical Analysis},
  Year                     = {2013},
  Number                   = {2},
  Pages                    = {539–554},
  Volume                   = {47},

  Keywords                 = {Coupled Surface and Subsurface, Navier-Stokes}
}

@InCollection{GiraultKanschatRiviere2013,
  Title                    = {On the coupling of incompressible Stokes or Navier–Stokes and Darcy flows through porous media},
  Author                   = {V. Girault and G. Kanschat and B. Riviere},
  Booktitle                = {Modelling and Simulation in Fluid Dynamics in Porous Media},
  Publisher                = {Springer},
  Year                     = {2013},
  Pages                    = {1–25},
  Keywords                 = {Coupled Surface and Subsurface, Discontinuous Galerkin, Navier-Stokes}
}

@Article{KeyesMcInnesWoodwardEtAl13,
  Title                    = {Multiphysics simulations: challenges and opportunities},
  Author                   = {David E. Keyes and Lois Curfman McInnes and Carol Woodward and William Gropp and Eric Myra and Michael Pernice and John Bell and Jed Brown and Alain Clo and Jeffrey Connors and Emil Constantinescu and Don Estep and Kate Evans and Charbel Farhat and Ammar Hakim and Glenn Hammond and Glen Hansen and Judith Hill and Tobin Isaac and Xiangmin Jiao and Kirk Jordan and Dinesh Kaushik and Efthimios Kaxiras and Alice Koniges and Kihwan Lee and Aaron Lott and Qiming Lu and John Magerlein and Reed Maxwell and Michael McCourt and Miriam Mehl and Roger Pawlowski and Amanda Peters Randles and Daniel Reynolds and Beatrice Riviere and Ulrich R\"{u}de and Tim Scheibe and John Shadid and Brendan Sheehan and Mark Shephard and Andrew Siegel and Barry Smith and Xianzhu Tang and Cian Wilson and Barbara Wohlmuth},
  Journal                  = {International Journal of High Performance Computing Applications},
  Year                     = {2013},

  Month                    = {Feb},
  Number                   = {1},
  Pages                    = {4–83},
  Volume                   = {27},

  Doi                      = {10.1177/1094342012468181},
  Keywords                 = {Coupled Surface and Subsurface}
}

@Article{LiuRiviere2013,
  Title                    = {Discontinuous Galerkin methods for elliptic partial differential equations with random coefficients},
  Author                   = {K. Liu and B. Riviere},
  Journal                  = {International Journal of Computer Mathematics},
  Year                     = {2013},
  Number                   = {11},
  Pages                    = {2477–2490},
  Volume                   = {90},

  Keywords                 = {Single-Phase Flow, Diffusion}
}

@InProceedings{Riviere2013,
  Title                    = {Discontinuous finite element methods for coupled surface-subsurface flow and transport problems},
  Author                   = {B. Riviere},
  Booktitle                = {IMA Volumes in Mathematics and its Applications: Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations},
  Year                     = {2013},
  Pages                    = {259–279},
  Publisher                = {Springer},

  Keywords                 = {Coupled Surface and Subsurface}
}

@Article{CesmeliogluRiviere2012,
  Title                    = {Existence of a weak solution for the fully coupled Navier–Stokes/Darcy-transport problem},
  Author                   = {A. Cesmelioglu and B. Riviere},
  Journal                  = {Journal of Differential Equations},
  Year                     = {2012},
  Pages                    = {4138–4175},
  Volume                   = {252},
  Doi			   = {10.1016/j.jde.2011.12.001},

  Keywords                 = {Coupled Surface and Subsurface, Navier-Stokes}
}

@Article{ChidyagwaiRiviereMishev,
  Title                    = {On the coupling of finite volume and discontinuous Galerkin method for elliptic problems},
  Author                   = {P. Chidyagwai and I. Mishev and B. Riviere},
  Journal                  = {Journal of Computational and Applied Mathematics},
  Year                     = {2011},
  Pages                    = {2193–2204},
  Volume                   = {231},
  Note			   = {Mistake in analysis, corrected in Riviere and Yang paper},

  Keywords                 = {Single-Phase Flow, Diffusion, Discontinuous Galerkin, Finite Volume}
}

@Article{ChidyagwaiRiviere2011,
  Title                    = {A two-grid method for coupled free flow with porous media flow},
  Author                   = {P. Chidyagwai and B. Riviere},
  Journal                  = {Advances in Water Resources},
  Year                     = {2011},
  Pages                    = {1113–1123},
  Volume                   = {34},

  Keywords                 = {Coupled Surface and Subsurface}
}

@Article{RiviereWalkington2011,
  Title                    = {Convergence of a discontinuous Galerkin method for the miscible displacement under low regularity},
  Author                   = {Riviere, Beatrice and Walkington, Noel},
  Journal                  = {SIAM Journal on Numerical Analysis},
  Year                     = {2011},
  Pages                    = {1085–1110},
  Volume                   = {49},

  Keywords                 = {Miscible Displacement}
}

@Article{WihlerRiviere2011,
  Title                    = {Discontinuous Galerkin methods for second-order elliptic PDE with low-regularity solutions},
  Author                   = {T. Wihler and B. Riviere},
  Journal                  = {Journal of Scientific Computing},
  Year                     = {2011},
  Number                   = {2},
  Pages                    = {151–165},
  Volume                   = {46},
  note			   = {DOI 10.1007/s10915-010-9387-9},

  Keywords                 = {Single-Phase Flow, Diffusion}
}

@InProceedings{YoungRiviere2011,
title={The Development of a Computational, Poroelastic Model of Intestinal Edema},
author={J. Young and B. Riviere},
booktitle={Proceedings of the ECCOMAS Thematic International Conference on Simulation and Modeling of Biological Flows},
year={2011},
Keywords={Intestinal Edema, Mathematical Biology}
}

@InProceedings{RiviereChidyagwaiMishev2010,
Title={On the Coupling of Finite Volume and Discontinuous Galerkin for Reservoir Simulation Problems},
Author={B. Riviere and P. Chidyagwai and I. Mishev},
booktitle={SPE Reservoir Symposium},
publisher={Society for Petroleum Engineers},
year={2011},
number={SPE-141971-MS},
Keywords           = {Finite Volume, Convection–Diffusion}
}

@Article{ChidyagwaiRiviere2010,
  Title                    = {Numerical modelling of coupled surface and subsurface flow systems},
  Author                   = {P. Chidyagwai and B. Riviere},
  Journal                  = {Advances in Water Resources},
  Year                     = {2010},
  Pages                    = {92–105},
  Volume                   = {33},

  Keywords                 = {Coupled Surface and Subsurface}
}

@Article{KanschatRiviere2010,
  Title                    = {A strongly conservative finite element method for the coupling of Stokes and Darcy flow},
  Author                   = {G. Kanschat and B. Riviere},
  Journal                  = {Journal of Computational Physics},
  Year                     = {2010},
  Number                   = {17},
  Pages                    = {5933–5943},
  Volume                   = {229},
  Keywords                 = {Coupled Surface and Subsurface}
}

@Article{CesmeliogluRiviere2009,
  Title                    = {Primal discontinuous Galerkin methods for time-dependent coupled surface and subsurface flow},
  Author                   = {A. Cesmelioglu and B. Riviere},
  Journal                  = {Journal of Scientific Computing},
  Year                     = {2009},
  Pages                    = {115–140},
  Volume                   = {40},

  Keywords                 = {Coupled Surface and Subsurface, Discontinuous Galerkin}
}

@Article{ChidyagwaiRiviere2009,
  Title                    = {On the solution of the coupled Navier–Stokes and Darcy equations},
  Author                   = {P. Chidyagwai and B. Riviere},
  Journal                  = {Computer Methods in Applied Mechanics and Engineering},
  Year                     = {2009},
  Pages                    = {3806–3820},
  Volume                   = {198},

  Keywords                 = {Coupled Surface and Subsurface, Navier-Stokes}
}

@Article{EpshteynKhanRiviere2009,
  Title                    = {Numerical solution of a one-dimensional inverse problem by the discontinuous Galerkin method},
  Author                   = {Y. Epshteyn and T. Khan and B. Riviere},
  Journal                  = {Mathematics and Computers in Simulation},
  Year                     = {2009},
  Pages                    = {1989–2000},
  Volume                   = {79},
  Doi			   = {10.1016/j.matcom.2008.08.002},
  Keywords		   = {Inverse Problems, Discontinuous Galerkin}
}

@Article{EpshteynRiviere2009,
  Title                    = {Analysis of hp discontinuous Galerkin methods for incompressible two-phase flow},
  Author                   = {Y. Epshteyn and B. Riviere},
  Journal                  = {Journal of Computational and Applied Mathematics},
  Year                     = {2009},
  Pages                    = {487–509},
  Volume                   = {225},
  Doi			   = {10.1016/j.cam.2008.08.026},

  Keywords                 = {Two-Phase Flow, Multiphase Flow, Discontinuous Galerkin}
}

@Article{GiraultRiviere2009,
  Title                    = {DG approximation of coupled Navier–Stokes and Darcy equations by Beaver–Joseph–Saffman interface condition},
  Author                   = {V. Girault and B. Riviere},
  Journal                  = {SIAM Journal on Numerical Analysis},
  Year                     = {2009},
  Pages                    = {2052–2089},
  Volume                   = {47},

  Keywords                 = {Coupled Surface and Subsurface, Discontinuous Galerkin, Navier-Stokes}
}

@Article{GuzmanRiviere2009,
  Title                    = {Sub-optimal convergence of non-symmetric discontinuous Galerkin methods for odd polynomial approximations},
  Author                   = {J. Guzman and B. Riviere},
  Journal                  = {Journal of Scientific Computing},
  Year                     = {2009},
  Pages                    = {273–280},
  Volume                   = {40},

  Keywords                 = {Single-Phase Flow, Diffusion, Discontinuous Galerkin}
}

@Article{ProftRiviere2009,
  Title                    = {Discontinuous Galerkin methods for convection–diffusion equations with varying and vanishing diffusivity},
  Author                   = {J. Proft and B. Riviere},
  Journal                  = {International Journal of Numerical Analysis and Modeling},
  Year                     = {2009},
  Pages                    = {533–561},
  Volume                   = {6},

  Keywords                 = {Transport, Convection–Diffusion}
}

@Article{RiviereEpshteynSwigonVodovotz2009,
  Title                    = {A simple mathematical model of signaling resulting from the binding of lipopolysaccharide with {T}oll-like receptor 4 demonstrates inherent preconditioning behavior},
  Author                   = {B. Riviere and Y. Epshteyn and D. Swigon and Y. Vodovotz},
  Journal                  = {Mathematical Biosciences},
  Year                     = {2009},
  Number                   = {1},
  Pages                    = {19–26},
  Volume                   = {217},
  Doi			   = {10.1016/j.mbs.2008.10.002},
  Keywords		   = {Signaling, Mathematical Biology}
}

@Article{CesmeliogluRiviere2008,
  Title                    = {Analysis of time-dependent Navier–Stokes flow coupled with Darcy flow},
  Author                   = {A. Cesmelioglu and B. Riviere},
  Journal                  = {Journal of Numerical Mathematics},
  Year                     = {2008},
  Number                   = {4},
  Pages                    = {249–280},
  Volume                   = {16},
  note			   = {DOI 10.1515/ JNUM.2008.012},

  Keywords                 = {Coupled Surface and Subsurface, Navier-Stokes}
}

@Article{EpshteynRiviere2008,
  Title                    = {Convergence of high order methods for miscible displacement},
  Author                   = {Y. Epshteyn and B. Riviere},
  Journal                  = {International Journal of Numerical Analysis and Modeling},
  Year                     = {2008},
  Pages                    = {47–63},
  Volume                   = {5},

  Keywords                 = {Miscible Displacement, Discontinuous Galerkin}
}

@Book{Riviere2008,
  Title                    = {Discontinuous Galerkin methods for solving elliptic and parabolic equations: theory and implementation},
  Author                   = {B. Riviere},
  Publisher                = {SIAM},
  Year                     = {2008},
  Keywords		   = {Book}
}

@Article{EpshteynRiviere2007,
  Title                    = {Estimation of penalty parameters for symmetric interior penalty Galerkin methods},
  Author                   = {Y. Epshteyn and B. Riviere},
  Journal                  = {Journal of Computational and Applied Mathematics},
  Year                     = {2007},
  Pages                    = {843–872},
  Volume                   = {206},
  Doi			   = {10.1016/j.cam.2006.08.029},

  Keywords                 = {Single-Phase Flow, Diffusion, Discontinuous Galerkin}
}

@Article{EpstheynRiviere2007-apnum,
  Title                    = {Fully implicit discontinuous finite element methods for two-phase flow},
  Author                   = {Y. Epshteyn and B. Riviere},
  Journal                  = {Applied Numerical Mathematics},
  Year                     = {2007},
  Pages                    = {383–401},
  Volume                   = {57},
  Doi			   = {10.1016/j.apnum.2006.04.004},

  Keywords                 = {Two-Phase Flow, Multiphase Flow, Discontinuous Galerkin}
}

@Article{MiRiviereClermontSteedVodovotz2007,
  Title                    = {Agent-based model of inflammation and wound healing: insights into diabetic foot ulcer pathology and the role of transforming growth factor-$\beta$ 1},
  Author                   = {Q. Mi and B. Riviere and G. Clermont and D.L. Steed and Y. Vodovotz},
  Journal                  = {Wound Repair and Regeneration},
  Year                     = {2007},
  Number                   = {5},
  Pages                    = {671–682},
  Volume                   = {15},
  Keywords		   = {Agent-Based Modeling},

  Doi                      = {10.1111/j.1524-475X.2007.00271.x}
}

@Article{MiSwigonRiviereCetinVodovotzHackam2007,
  Title                    = {One-dimensional elastic continuum model of enterocyte layer migration},
  Author                   = {Q. Mi and D. Swigon and B. Riviere and S. Cetin and Y. Vodovotz and D. Hackam},
  Journal                  = {Biophysical Journal},
  Year                     = {2007},
  Pages                    = {3745–3752},
  Volume                   = {93},
  Keywords		   = {Wave, Cell Motility, Hyperbolic}
}

@Article{MiSwigonRiviere2007,
  Title                    = {Two-dimensional elastic continuum model of enterocyte layer migration},
  Author                   = {Q. Mi and D. Swigon and B. Riviere},
  Journal                  = {Journal of Critical Care},
  Year                     = {2007},
  Pages                    = {350-},
  Volume                   = {22},
  Keywords		   = {Wave, Cell Motility, Hyperbolic}
}

@Article{RiviereEpshteynSwigonVodovotz2007,
  Title                    = {A simple mathematical model of lipopolysaccharide signaling through {T}oll-like receptor 4 results in complex insights on preconditioning},
  Author                   = {Y. Epshteyn and B. Riviere and D. Swigon and Y. Vodovotz},
  Journal                  = {Journal of Critical Care},
  Year                     = {2007},
  Pages                    = {333–335},
  Volume                   = {22},
  Keywords		   = {Signaling, Mathematical Biology}

}

@Article{RiviereShawWhiteman2007,
  Title                    = {Discontinuous Galerkin finite element methods for dynamic linear solid viscoelasticity},
  Author                   = {B. Riviere and S. Shaw and J.R. Whiteman},
  Journal                  = {Numerical Methods for Partial Differential Equations},
  Year                     = {2007},
  Number                   = {5},
  Pages                    = {1149–1166},
  Volume                   = {23},
  Keywords		   = {Viscoelasticity}
}

@Article{EpstheynRiviere2006,
  Title                    = {On the solution of incompressible two-phase flow by a p-version discontinuous Galerkin method},
  Author                   = {Y. Epshteyn and B. Riviere},
  Journal                  = {Communications in Numerical Methods in Engineering},
  Year                     = {2006},
  Pages                    = {741–751},
  Volume                   = {22},

  Keywords                 = {Two-Phase Flow, Multiphase Flow, Discontinuous Galerkin}
}

@Article{KayaLaytonRiviere2006,
  Title                    = {Subgrid stabilized defect correction methods for the Navier–Stokes equations},
  Author                   = {S. Kaya and W. Layton and B. Riviere},
  Journal                  = {SIAM Journal on Numerical Analysis},
  Year                     = {2006},
  Number                   = {4},
  Pages                    = {1639–1654},
  Volume                   = {44},
  Keywords                 = {Navier-Stokes}
}

@Article{KayaRiviere2006,
  Title                    = {A two-grid stabilization method for solving the steady-state Navier–Stokes equations},
  Author                   = {S. Kaya and B. Riviere},
  Journal                  = {Numerical Methods for Partial Differential Equations},
  Year                     = {2006},
  Number                   = {3},
  Pages                    = {728–743},
  Volume                   = {22},
  Keywords                 = {Navier–Stokes}
}

@Article{KlieberRiviere2006,
  Title                    = {Adaptive simulations of two-phase flow by discontinuous Galerkin methods},
  Author                   = {W. Klieber and B. Riviere},
  Journal                  = {Computer Methods in Applied Mechanics and Engineering},
  Year                     = {2006},
  Pages                    = {404–419},
  Volume                   = {196},

  Keywords                 = {Two-Phase Flow, Multiphase Flow, Discontinuous Galerkin}
}

@Article{RiviereGirault2006,
  Title                    = {Discontinuous finite element methods for incompressible flows on subdomains with non-matching interfaces},
  Author                   = {B. Riviere and V. Girault},
  Journal                  = {Computer Methods in Applied Mechanics and Engineering},
  Year                     = {2006},
  Pages                    = {3274–3292},
  Volume                   = {195},
  Doi			   = {10.1016/j.cma.2005.06.014},

  Keywords                 = {Navier–Stokes}
}

@Article{RiviereShaw2006,
  Title                    = {Discontinuous Galerkin finite element approximation of nonlinear non-Fickian diffusion in viscoelastic polymers},
  Author                   = {B. Riviere and S. Shaw},
  Journal                  = {SIAM Journal on Numerical Analysis},
  Year                     = {2006},
  Number                   = {6},
  Pages                    = {2650–2670},
  Volume                   = {44},
  Keywords		   = {Viscoelasticity}
}

@InProceedings{EphsteynRiviere2006,
  Title                    = {Fully Implicit Discontinuous Galerkin Scheme for Two-Phase Flow},
  Author                   = {Y. Epshteyn and B. Riviere},
  Booktitle                = {Proceedings of the MSRI workshop ``The legacy of Ladyzhenskaya and Oleinik"},
  Year                     = {2006},
  Pages                    = {125–128},

  Keywords                 = {Two-Phase Flow, Multiphase Flow}
}

@Article{GiraultRiviereWheeler2005,
  Title                    = {A discontinuous Galerkin method with nonoverlapping domain decomposition for the Stokes and Navier–Stokes problems},
  Author                   = {V. Girault and B. Riviere and M.F. Wheeler},
  Journal                  = {Mathematics of Computation},
  Year                     = {2005},
  Number                   = {249},
  Pages                    = {53–84},
  Volume                   = {74},

  Keywords                 = {Stokes, Navier–Stokes, Discontinuous Galerkin}
}

@Article{GiraultRiviereWheeler2005-esaim,
  Title                    = {A splitting method using discontinuous Galerkin for the transient incompressible Navier–Stokes equations},
  Author                   = {V. Girault and B. Riviere and M.F. Wheeler},
  Journal                  = {ESAIM: Mathematical Modelling and Numerical Analysis},
  Year                     = {2005},
  Number                   = {06},
  Pages                    = {1115–1147},
  Volume                   = {39},

  Keywords                 = {Navier–Stokes, Discontinuous Galerkin},
  Publisher                = {Cambridge Univ Press}
}

@Article{KayaRiviere2005,
  Title                    = {A discontinuous subgrid eddy viscosity method for the time-dependent Navier–Stokes equations},
  Author                   = {S. Kaya and B. Riviere},
  Journal                  = {SIAM Journal on Numerical Analysis},
  Year                     = {2005},
  Number                   = {4},
  Pages                    = {1572–1595},
  Volume                   = {43},

  Keywords                 = {Navier–Stokes, Turbulence, Discontinuous Galerkin}
}

@Article{Riviere2005,
  Title                    = {Analysis of a discontinuous finite element method for the coupled Stokes and Darcy problems},
  Author                   = {B. Riviere},
  Journal                  = {Journal of Scientific Computing},
  Year                     = {2005},
  Number                   = {1},
  Pages                    = {479–500},
  Volume                   = {22},
  Keywords		   = {Coupled Surface and Subsurface}
}

@InProceedings{VodovotzChowBartelsLagoa,
  Title                    = {Mathematical simulations of sepsis and trauma},
  Author                   = {Y. Vodovotz and C. Chow and J. Bartels and C. Lagoa and R. Kumar and J. Day and J. Rubin and B. Ermentrout  and B. Riviere and I. Yotov and G. Constantine and T. Billiar and M. Fink and G. Clermont},
  Booktitle                = {Proceedings of the 11th Congress of the European Shock Society},
  Year                     = {2005},
  Pages                    = {151–159},

  Keywords                 = {Mathematical Biology}
}

@Article{RiviereYotov2005,
  Title                    = {Locally conservative coupling of Stokes and Darcy flow},
  Author                   = {B. Riviere and I. Yotov},
  Journal                  = {SIAM J. Numer. Anal.},
  Year                     = {2005},
  Pages                    = {1959–1977},
  Volume                   = {42},

  Keywords                 = {Coupled Surface and Subsurface}
}

@Article{Riviere2004,
  Title                    = {Analysis of a multi-numerics/multi-physics problem},
  Author                   = {B. Riviere},
  Journal                  = {Numerical Mathematics and Advanced Applications},
  Year                     = {2004},
  Pages                    = {726–735},

  Keywords                 = {Coupled Surface and Subsurface}
}

@InProceedings{Riviere2004-eccomas,
  Title                    = {Numerical study of a discontinuous {G}alerkin method for incompressible two-phase flow},
  Author                   = {B. Riviere},
  Booktitle                = {ECCOMAS Proceedings},
  Year                     = {2004},
  Keywords		   = {Two-Phase Flow, Multiphase Flow}
}

@Article{BastianRiviere2003,
  Title                    = {Superconvergence and H(div) projection for discontinuous Galerkin methods},
  Author                   = {P. Bastian and B. Riviere},
  Journal                  = {International Journal for Numerical Methods in Fluids},
  Year                     = {2003},
  Pages                    = {1043–1057},
  Volume                   = {42},

  Keywords                 = {Single-Phase Flow, Diffusion, Discontinuous Galerkin}
}

@Article{RiviereShawWheelerWhiteman2003,
  Title                    = {Discontinuous Galerkin finite element methods for linear elasticity and quasistatic linear viscoelasticity},
  Author                   = {B. Riviere and S. Shaw and M.F. Wheeler and J.R. Whiteman},
  Journal                  = {Numerische Mathematik},
  Year                     = {2003},
  Number                   = {2},
  Pages                    = {347–376},
  Volume                   = {95},
  Keywords		   = {Elasticity,Viscoelasticity}
}

@Article{RiviereWheeler2003,
  Title                    = {A posteriori error estimates and mesh adaptation strategy for discontinuous Galerkin methods applied to diffusion problems},
  Author                   = {B. Riviere and M.F. Wheeler},
  Journal                  = {Computers \& Mathematics with Applications},
  Year                     = {2003},
  Number                   = {1},
  Pages                    = {141–163},
  Volume                   = {46},

  Keywords                 = {Single-Phase Flow, Diffusion}
}

@Article{RiviereWheeler2003-cont,
  Title                    = {Discontinuous finite element methods for acoustic and elastic wave problems},
  Author                   = {B. Riviere and M.F. Wheeler},
  Journal                  = {Contemporary Mathematics},
  Year                     = {2003},
  Pages                    = {271–282},
  Volume                   = {329},
  Keywords		   = {Wave, Hyperbolic}
}

@Article{JenkinsRiviereWheeler2002,
  Title                    = {A priori error estimates for mixed finite element approximations of the acoustic wave equation},
  Author                   = {E.W. Jenkins and B. Riviere and M.F. Wheeler},
  Journal                  = {SIAM Journal on Numerical Analysis},
  Year                     = {2002},
  Number                   = {5},
  Pages                    = {1698–1715},
  Volume                   = {40},
  Keywords		   = {Wave, Hyperbolic, Mixed Finite Element}
}

@InProceedings{RiviereWheelerProc2002,
  Title                    = {Miscible displacement in porous media},
  Author                   = {B. Riviere and M.F. Wheeler},
  Booktitle                = {Proceedings of the XIV International Conference on Computational Methods in Water Resources},
  Year                     = {2002},
  volume		   = {47},
  Pages                    = {907–914},

  Keywords                 = {Miscible Displacement}
}

@InProceedings{GuillotRiviereWheelerProc2002,
  Title                    = {Discontinuous Galerkin Methods for Mass Conservation Equations for Environmental Modeling},
  Author                   = {M. Guillot and B. Riviere and M.F. Wheeler},
  Booktitle                = {Proceedings of the XIV International Conference on Computational Methods in Water Resources},
  Year                     = {2002},
  volume		   = {47},
  Pages                    = {939–946},

  Keywords                 = {Transport}
}

@InProceedings{WheelerPeszynskaRiviere,
  Title                    = {Computational Science Issues in Modeling Oil and Gas Production},
  Author                   = {M.F. Wheeler and M. Peszynska and B. Riviere},
  Booktitle                = {Proceedings of the 8th European Conference on the Mathematics of Oil Recovery-ECMOR VIII},
  Year                     = {2002},
  Publisher		   = {EAGE},
  Keywords		   = {Multiphase Flow}
}

@Article{RiviereWheeler2002-comm,
  Title                    = {Discontinuous Galerkin methods for flow and transport problems in porous media},
  Author                   = {B. Riviere and M.F. Wheeler},
  Journal                  = {Communications in Numerical Methods in Engineering},
  Year                     = {2002},
  Pages                    = {63–68},
  Volume                   = {18},

  Keywords                 = {Miscible Displacement}
}

@Article{RiviereWheeler2002-compgeo,
  Title                    = {Coupling locally conservative methods for single phase flow},
  Author                   = {B. Riviere and M.F. Wheeler},
  Journal                  = {Computational Geosciences},
  Year                     = {2002},
  Pages                    = {269–284},
  Volume                   = {6},

  Keywords                 = {Single-Phase Flow, Diffusion}
}

@InProceedings{RiviereWheeler2002-cont,
  Title                    = {Non conforming methods for transport with nonlinear reaction},
  Author                   = {B. Riviere and M.F. Wheeler},
  Booktitle                = {Fluid Flow and Transport in Porous Media: Mathematical and Numerical Treatment},
  Year                     = {2002},
  Editor                   = {Z. Chen and R. Ewing},
  Pages                    = {421–430},
  Series                   = {Contemporary Mathematics},
  Volume                   = {295},

  Keywords                 = {Transport, Convection–Diffusion}
}

@InCollection{SunRiviereWheeler2002,
  Title                    = {A combined mixed finite element and discontinuous Galerkin method for miscible displacement problem in porous media},
  Author                   = {S. Shuyu and B. Riviere and M.F. Wheeler},
  Booktitle                = {Recent progress in computational and applied PDEs},
  Publisher                = {Springer},
  Year                     = {2002},
  Pages                    = {323–351},

  Keywords                 = {Miscible Displacement}
}

@InProceedings{WheelerEslingerSunRiviere,
title={Discontinuous Galerkin Method for Modeling Flow and Reactive Transport in Porous Media},
author={M.F. Wheeler and O. Eslinger and S. Sun and B. Riviere},
booktitle={Proceedings of the 2002 CANUM Conference},
year={2002},
Keywords={Transport, Miscible Displacement}
}

@Article{RiviereWheelerGirault2001,
  Title                    = {A priori error estimates for finite element methods based on discontinuous approximation spaces for elliptic problems},
  Author                   = {B. Riviere and M.F. Wheeler and V. Girault},
  Journal                  = {SIAM Journal on Numerical Analysis},
  Year                     = {2001},
  Number                   = {3},
  Pages                    = {902–931},
  Volume                   = {39},

  Keywords                 = {Single-Phase Flow, Diffusion}
}

@InProceedings{RiviereWheeler2000,
  Title                    = {Locally conservative algorithms for flow},
  Author                   = {B. Riviere and M.F. Wheeler},
  Booktitle                = {MAFELAP 1999 Proceedings},
  Year                     = {2000},
  Pages                    = {29–46},

  Keywords                 = {Miscible Displacement}
}

@Article{RiviereWheelerBanas2000,
  Title                    = {Part II. Discontinuous Galerkin method applied to a single phase flow in porous media},
  Author                   = {B. Riviere and M.F. Wheeler and K. Banas},
  Journal                  = {Computational Geosciences},
  Year                     = {2000},
  Pages                    = {337–349},
  Volume                   = {4},

  Keywords                 = {Single-Phase Flow, Diffusion}
}

@InProceedings{RiviereWheeler1999,
  Title                    = {A discontinuous Galerkin method applied to nonlinear parabolic equations},
  Author                   = {B. Riviere and M.F. Wheeler},
  Booktitle                = {Discontinuous Galerkin Methods: Theory, Computation and Applications},
  Year                     = {1999},
  Pages                    = {231–244},
  Volume                   = {11},

  Keywords                 = {Transport, Convection–Diffusion, Parabolic}
}

@Article{RiviereWheelerGirault1999,
  Title                    = {Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. Part I},
  Author                   = {B. Riviere and M.F. Wheeler and V. Girault},
  Journal                  = {Computational Geosciences},
  Year                     = {1999},

  Month                    = {April},
  Pages                    = {337–360},
  Volume                   = {3},

  Annote                   = {Baltzer Science Publishers},
  Keywords                 = {Single-Phase Flow, Diffusion}
}

@InProceedings{BakerGunnelsMorrowRiviereVandeGeijn1998,
  Title                    = {High performance through high level abstraction},
  Author                   = {G. Baker and J. Gunnels and G. Morrow and B. Riviere and R. Van de Geijn},
  Booktitle                = {Proceedings of the 1998 International Conference on Parallel Processing},
  Year                     = {1998},
  Keywords		   = {Solvers}
}