A Remark on the A Posteriori Error Analysis of Discontinuous Galerkin Methods
for the Obstacle Problem

Thirupathi Gudi; Kamana Porwal

doi:10.1515/cmam-2013-0015

Published by De Gruyter August 13, 2013

A Remark on the A Posteriori Error Analysis of Discontinuous Galerkin Methods for the Obstacle Problem

Thirupathi Gudi and Kamana Porwal

From the journal Computational Methods in Applied Mathematics

https://doi.org/10.1515/cmam-2013-0015

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Abstract.

We revisit the a posteriori error analysis of discontinuous Galerkin methods for the obstacle problem derived in [Math. Comput. (2013), DOI 10.1090/S0025-5718-2013-02728-7]. Under a mild assumption on the trace of obstacle, we derive a reliable a posteriori error estimator which does not involve min/max functions. A key in this approach is an auxiliary problem with discrete obstacle. Applications to various discontinuous Galerkin finite element methods are presented. Numerical experiments show that the new estimator obtained in this article performs better.

Keywords: Finite Element; Discontinuous Galerkin; A Posteriori Error Estimate; Obstacle Problem; Variational Inequalities

MSC: 65N30; 65N15

Published Online: 2013-08-13

Published in Print: 2014-01-01

A Remark on the A Posteriori Error Analysis of Discontinuous Galerkin Methods for the Obstacle Problem

Abstract.

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