scholarly journals Pre-asymptotic error analysis of hp-interior penalty discontinuous Galerkin methods for the Helmholtz equation with large wave number

2015 ◽  
Vol 70 (5) ◽  
pp. 917-933 ◽  
Author(s):  
Lingxue Zhu ◽  
Yu Du
Keyword(s):  
Error Analysis ◽  
Helmholtz Equation ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Methods ◽  
Wave Number ◽  
Galerkin Methods ◽  
Large Wave ◽  
Asymptotic Error ◽  
Large Wave Number ◽  
Asymptotic 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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