@article{LeeWhe2016_EG,
title = "Adaptive enriched Galerkin methods for miscible displacement problems with entropy residual stabilization",
journal = "Journal of Computational Physics ",
volume = "331",
number = "",
pages = "19 - 37",
year = "2017",
note = "",
issn = "0021-9991",
doi = "http://dx.doi.org/10.1016/j.jcp.2016.10.072",
url = "http://www.sciencedirect.com/science/article/pii/S0021999116305952",
author = "Sanghyun Lee and Mary F. Wheeler",
keywords = {Porous media, Enriched Galerkin,
Miscible displacement,
Viscous fingering,
Locally conservative,
Entropy viscosity,
Hele-Shaw,
Adaptive finite elements}, 
abstract = "We present a novel approach to the simulation of miscible displacement by employing adaptive enriched Galerkin finite element methods (EG) coupled with entropy residual stabilization for transport. In particular, numerical simulations of viscous fingering instabilities in heterogeneous porous media and Hele–Shaw cells are illustrated. EG is formulated by enriching the conforming continuous Galerkin finite element method (CG) with piecewise constant functions. The method provides locally and globally conservative fluxes, which are crucial for coupled flow and transport problems. Moreover, EG has fewer degrees of freedom in comparison with discontinuous Galerkin (DG) and an efficient flow solver has been derived which allows for higher order schemes. Dynamic adaptive mesh refinement is applied in order to reduce computational costs for large-scale three dimensional applications. In addition, entropy residual based stabilization for high order EG transport systems prevents spurious oscillations. Numerical tests are presented to show the capabilities of EG applied to flow and transport."
}

{"_id":"76AQZGJRdnsHGMsAk","bibbaseid":"lee-wheeler-adaptiveenrichedgalerkinmethodsformiscibledisplacementproblemswithentropyresidualstabilization-2017","author_short":["Lee, S.","Wheeler, M. F."],"bibdata":{"bibtype":"article","type":"article","title":"Adaptive enriched Galerkin methods for miscible displacement problems with entropy residual stabilization","journal":"Journal of Computational Physics ","volume":"331","number":"","pages":"19 - 37","year":"2017","note":"","issn":"0021-9991","doi":"http://dx.doi.org/10.1016/j.jcp.2016.10.072","url":"http://www.sciencedirect.com/science/article/pii/S0021999116305952","author":[{"firstnames":["Sanghyun"],"propositions":[],"lastnames":["Lee"],"suffixes":[]},{"firstnames":["Mary","F."],"propositions":[],"lastnames":["Wheeler"],"suffixes":[]}],"keywords":"Porous media, Enriched Galerkin, Miscible displacement, Viscous fingering, Locally conservative, Entropy viscosity, Hele-Shaw, Adaptive finite elements","abstract":"We present a novel approach to the simulation of miscible displacement by employing adaptive enriched Galerkin finite element methods (EG) coupled with entropy residual stabilization for transport. In particular, numerical simulations of viscous fingering instabilities in heterogeneous porous media and Hele–Shaw cells are illustrated. EG is formulated by enriching the conforming continuous Galerkin finite element method (CG) with piecewise constant functions. The method provides locally and globally conservative fluxes, which are crucial for coupled flow and transport problems. Moreover, EG has fewer degrees of freedom in comparison with discontinuous Galerkin (DG) and an efficient flow solver has been derived which allows for higher order schemes. Dynamic adaptive mesh refinement is applied in order to reduce computational costs for large-scale three dimensional applications. In addition, entropy residual based stabilization for high order EG transport systems prevents spurious oscillations. Numerical tests are presented to show the capabilities of EG applied to flow and transport.","bibtex":"@article{LeeWhe2016_EG,\ntitle = \"Adaptive enriched Galerkin methods for miscible displacement problems with entropy residual stabilization\",\njournal = \"Journal of Computational Physics \",\nvolume = \"331\",\nnumber = \"\",\npages = \"19 - 37\",\nyear = \"2017\",\nnote = \"\",\nissn = \"0021-9991\",\ndoi = \"http://dx.doi.org/10.1016/j.jcp.2016.10.072\",\nurl = \"http://www.sciencedirect.com/science/article/pii/S0021999116305952\",\nauthor = \"Sanghyun Lee and Mary F. Wheeler\",\nkeywords = {Porous media, Enriched Galerkin,\nMiscible displacement,\nViscous fingering,\nLocally conservative,\nEntropy viscosity,\nHele-Shaw,\nAdaptive finite elements}, \nabstract = \"We present a novel approach to the simulation of miscible displacement by employing adaptive enriched Galerkin finite element methods (EG) coupled with entropy residual stabilization for transport. In particular, numerical simulations of viscous fingering instabilities in heterogeneous porous media and Hele–Shaw cells are illustrated. EG is formulated by enriching the conforming continuous Galerkin finite element method (CG) with piecewise constant functions. The method provides locally and globally conservative fluxes, which are crucial for coupled flow and transport problems. Moreover, EG has fewer degrees of freedom in comparison with discontinuous Galerkin (DG) and an efficient flow solver has been derived which allows for higher order schemes. Dynamic adaptive mesh refinement is applied in order to reduce computational costs for large-scale three dimensional applications. In addition, entropy residual based stabilization for high order EG transport systems prevents spurious oscillations. Numerical tests are presented to show the capabilities of EG applied to flow and transport.\"\n}\n\n","author_short":["Lee, S.","Wheeler, M. F."],"key":"LeeWhe2016_EG","id":"LeeWhe2016_EG","bibbaseid":"lee-wheeler-adaptiveenrichedgalerkinmethodsformiscibledisplacementproblemswithentropyresidualstabilization-2017","role":"author","urls":{"Paper":"http://www.sciencedirect.com/science/article/pii/S0021999116305952"},"keyword":["Porous media","Enriched Galerkin","Miscible displacement","Viscous fingering","Locally conservative","Entropy viscosity","Hele-Shaw","Adaptive finite elements"],"metadata":{"authorlinks":{}},"html":""},"bibtype":"article","biburl":"https://www.math.fsu.edu/~lee/mypub.bib","dataSources":["457QZEBmqtBCSsjgP"],"keywords":["porous media","enriched galerkin","miscible displacement","viscous fingering","locally conservative","entropy viscosity","hele-shaw","adaptive finite elements"],"search_terms":["adaptive","enriched","galerkin","methods","miscible","displacement","problems","entropy","residual","stabilization","lee","wheeler"],"title":"Adaptive enriched Galerkin methods for miscible displacement problems with entropy residual stabilization","year":2017}