scholarly journals Discontinuous Galerkin methods on hp-anisotropic meshes I: a priori error analysis

2007 ◽  
Vol 1 (2/3/4) ◽  
pp. 221 ◽  
Author(s):  
Emmanuil H. Georgoulis ◽  
Edward Hall ◽  
Paul Houston
Keyword(s):  
Error Analysis ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Methods ◽  
A Priori ◽  
Galerkin Methods ◽  
Anisotropic Meshes ◽  
A Priori Error Analysis

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.

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