@article{Chaudhry2015730,
title = "A {P}osteriori {E}rror {A}nalysis of {IMEX} {M}ulti-{S}tep {T}ime {I}ntegration {M}ethods for {A}dvection-{D}iffusion-{R}eaction {E}quations ",
journal = "Computer Methods in Applied Mechanics and Engineering ",
volume = "285",
number = "",
pages = "730-751",
year = "2015",
note = "",
issn = "0045-7825",
doi = "http://dx.doi.org/10.1016/j.cma.2014.11.015",
url = "http://www.sciencedirect.com/science/article/pii/S0045782514004411",
author = "J. Chaudhry and D. Estep and V. Ginting and J. Shadid and S. Tavener",
keywords = "Error estimation",
keywords = "Adjoint operator",
keywords = "Implicit–explicit schemes ",
abstract = "Implicit-Explicit (IMEX) schemes are an important and widely used class of time integration methods for both parabolic and hyperbolic partial differential equations. We develop accurate a posteriori error estimates for a user-defined quantity of interest for two classes of multi-step IMEX schemes for advection-diffusion-reaction problems. The analysis proceeds by recasting the IMEX schemes into a variational form suitable for a posteriori error analysis employing adjoint problems and computable residuals. The a posteriori estimates quantify distinct contributions from various aspects of the spatial and temporal discretizations, and can be used to evaluate discretization choices. Numerical results are presented that demonstrate the accuracy of the estimates for a representative set of problems. "
}

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We develop accurate a posteriori error estimates for a user-defined quantity of interest for two classes of multi-step IMEX schemes for advection-diffusion-reaction problems. The analysis proceeds by recasting the IMEX schemes into a variational form suitable for a posteriori error analysis employing adjoint problems and computable residuals. The a posteriori estimates quantify distinct contributions from various aspects of the spatial and temporal discretizations, and can be used to evaluate discretization choices. Numerical results are presented that demonstrate the accuracy of the estimates for a representative set of problems. ","bibtex":"@article{Chaudhry2015730,\ntitle = \"A {P}osteriori {E}rror {A}nalysis of {IMEX} {M}ulti-{S}tep {T}ime {I}ntegration {M}ethods for {A}dvection-{D}iffusion-{R}eaction {E}quations \",\njournal = \"Computer Methods in Applied Mechanics and Engineering \",\nvolume = \"285\",\nnumber = \"\",\npages = \"730-751\",\nyear = \"2015\",\nnote = \"\",\nissn = \"0045-7825\",\ndoi = \"http://dx.doi.org/10.1016/j.cma.2014.11.015\",\nurl = \"http://www.sciencedirect.com/science/article/pii/S0045782514004411\",\nauthor = \"J. Chaudhry and D. Estep and V. Ginting and J. Shadid and S. Tavener\",\nkeywords = \"Error estimation\",\nkeywords = \"Adjoint operator\",\nkeywords = \"Implicit–explicit schemes \",\nabstract = \"Implicit-Explicit (IMEX) schemes are an important and widely used class of time integration methods for both parabolic and hyperbolic partial differential equations. We develop accurate a posteriori error estimates for a user-defined quantity of interest for two classes of multi-step IMEX schemes for advection-diffusion-reaction problems. The analysis proceeds by recasting the IMEX schemes into a variational form suitable for a posteriori error analysis employing adjoint problems and computable residuals. The a posteriori estimates quantify distinct contributions from various aspects of the spatial and temporal discretizations, and can be used to evaluate discretization choices. 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