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

Thirupathi Gudi 1  and Kamana Porwal 2
  • 1 Department of Mathematics, Indian Institute of Science, Bangalore 560012, India
  • 2 Department of Mathematics, Indian Institute of Science, Bangalore 560012, India

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.

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