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A POSTERIORI ERROR CONTROL OF DISCONTINUOUS GALERKIN METHODS FOR ELLIPTIC OBSTACLE PROBLEMS

Gudi, Thirupathi and Porwal, Kamana (2014) A POSTERIORI ERROR CONTROL OF DISCONTINUOUS GALERKIN METHODS FOR ELLIPTIC OBSTACLE PROBLEMS. In: MATHEMATICS OF COMPUTATION, 83 (286). pp. 579-602.

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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.

Item Type: Journal Article
Additional Information: copyright for this article belongs to AMER MATHEMATICAL SOC, USA
Keywords: Finite element; discontinuous Galerkin; a posteriori error estimate; obstacle problem; variational inequalities; Lagrange multiplier
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 27 Jan 2014 06:15
Last Modified: 27 Jan 2014 06:15
URI: http://eprints.iisc.ac.in/id/eprint/48246

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