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A Remark on the A Posteriori Error Analysis of Discontinuous Galerkin Methods for the Obstacle Problem
-
Thirupathi Gudi
and
Kamana Porwal
Published/Copyright:
August 13, 2013
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
Published Online: 2013-08-13
Published in Print: 2014-01-01
© 2014 by Walter de Gruyter Berlin/Boston
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Articles in the same Issue
- Frontmatter
- Mixed Finite Element Analysis of Eigenvalue Problems on Curved Domains
- Computational Survey on A Posteriori Error Estimators for the Crouzeix–Raviart Nonconforming Finite Element Method for the Stokes Problem
- High Order Numerical Methods for Fractional Terminal Value Problems
- A Remark on the A Posteriori Error Analysis of Discontinuous Galerkin Methods for the Obstacle Problem
- Black-Box Hartree–Fock Solver by Tensor Numerical Methods
- Combined Error Estimates in the Case of Dimension Reduction
Keywords for this article
Finite Element;
Discontinuous Galerkin;
A Posteriori Error Estimate;
Obstacle Problem;
Variational Inequalities
Articles in the same Issue
- Frontmatter
- Mixed Finite Element Analysis of Eigenvalue Problems on Curved Domains
- Computational Survey on A Posteriori Error Estimators for the Crouzeix–Raviart Nonconforming Finite Element Method for the Stokes Problem
- High Order Numerical Methods for Fractional Terminal Value Problems
- A Remark on the A Posteriori Error Analysis of Discontinuous Galerkin Methods for the Obstacle Problem
- Black-Box Hartree–Fock Solver by Tensor Numerical Methods
- Combined Error Estimates in the Case of Dimension Reduction
