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L2(H1 Norm A PosterioriError Estimation for Discontinuous Galerkin Approximations of Reactive Transport Problems

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Abstract

Explicita posteriori residual type error estimators in L2(H1) norm are derived for discontinuous Galerkin (DG) methods applied to transport in porous media with general kinetic reactions. They are flexible and apply to all the four primal DG schemes, namely, Oden–Babuška–Baumann DG (OBB-DG), non-symmetric interior penalty Galerkin (NIPG), symmetric interior penalty Galerkin (SIPG) and incomplete interior penalty Galerkin (IIPG). The error estimators use directly all the available information from the numerical solution and can be computed efficiently. Numerical examples are presented to demonstrate the efficiency and the effectivity of these theoretical estimators.

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Authors and Affiliations

  1. The Center for Subsurface Modeling (CSM), The Institute for Computational Engineering and Sciences (ICES), The University of Texas, Austin, Texas, 78712, USA

    Shuyu Sun & Mary F. Wheeler

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  1. Shuyu Sun
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  2. Mary F. Wheeler
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The authors would like to thank the anonymous referees for their incisive suggestions which contributed toward improving the paper.

AMS subject classifications:65M15;65M60;65M50.

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Sun, S., Wheeler, M.F. L2(H1 Norm A PosterioriError Estimation for Discontinuous Galerkin Approximations of Reactive Transport Problems. J Sci Comput 22, 501–530 (2005). https://doi.org/10.1007/s10915-004-4148-2

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