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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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A posteriori error control of discontinuous Galerkin methods for elliptic obstacle problems
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by Thirupathi Gudi and Kamana Porwal PDF
Math. Comp. 83 (2014), 579-602 Request permission

Abstract:

In this article, we derive an a posteriori error estimator for various discontinuous Galerkin (DG) methods that are proposed in (Wang, Han and Cheng, SIAM J. Numer. Anal., 48:708–733, 2010) for an elliptic obstacle problem. Using a key property of DG methods, we perform the analysis in a general framework. The error estimator we have obtained for DG methods is comparable with the estimator for the conforming Galerkin (CG) finite element method. In the analysis, we construct a non-linear smoothing function mapping DG finite element space to CG finite element space and use it as a key tool. The error estimator consists of a discrete Lagrange multiplier associated with the obstacle constraint. It is shown for non-over-penalized DG methods that the discrete Lagrange multiplier is uniformly stable on non-uniform meshes. Finally, numerical results demonstrating the performance of the error estimator are presented.
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Additional Information
  • Thirupathi Gudi
  • Affiliation: Department of Mathematics, Indian Institute of Science, Bangalore - 560012, India
  • Email: gudi@math.iisc.ernet.in
  • Kamana Porwal
  • Affiliation: Department of Mathematics, Indian Institute of Science, Bangalore - 560012, India
  • Email: kamana@math.iisc.ernet.in
  • Received by editor(s): November 1, 2011
  • Received by editor(s) in revised form: April 3, 2012, and June 18, 2012
  • Published electronically: June 19, 2013
  • Additional Notes: The first author’s work is supported by the UGC Center for Advanced Study
    The second author’s work is supported in part by the UGC center for Advanced Study and in part by the Council of Scientific and Industrial Research (CSIR)
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 83 (2014), 579-602
  • MSC (2010): Primary 65N30, 65N15
  • DOI: https://doi.org/10.1090/S0025-5718-2013-02728-7
  • MathSciNet review: 3143685