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

2014 ◽  
Vol 14 (1) ◽  
pp. 71-87 ◽  
Author(s):  
Thirupathi Gudi ◽  
Kamana Porwal
Keyword(s):  
Error Analysis ◽  
Discontinuous Galerkin ◽  
Obstacle Problem ◽  
Discontinuous Galerkin Methods ◽  
Auxiliary Problem ◽  
Posteriori Error ◽  
Error Estimator ◽  
Galerkin Methods ◽  
A Posteriori ◽  
Posteriori Error Analysis

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.

A Priori and a Posteriori Error Analysis of the Discontinuous Galerkin Methods for Reissner-Mindlin Plates

2011 ◽  
Vol 3 (6) ◽  
pp. 649-662 ◽  
Author(s):  
Jun Hu ◽  
Yunqing Huang
Keyword(s):  
Discontinuous Galerkin ◽  
Error Control ◽  
Discontinuous Galerkin Methods ◽  
A Priori ◽  
Posteriori Error ◽  
Mindlin Plate ◽  
Galerkin Methods ◽  
A Posteriori ◽  
A Posteriori Error ◽  
Posteriori Error Analysis

AbstractIn this paper, we apply an a posteriori error control theory that we develop in a very recent paper to three families of the discontinuous Galerkin methods for the Reissner-Mindlin plate problem. We derive robust a posteriori error estimators for them and prove their reliability and efficiency.

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