Conforming and discontinuous Galerkin FEM in space for solving parabolic obstacle problem

2019 ◽  
Vol 78 (12) ◽  
pp. 3896-3915 ◽  
Author(s):  
Thirupathi Gudi ◽  
Papri Majumder
Keyword(s):  
Discontinuous Galerkin ◽  
Obstacle Problem ◽  
Discontinuous Galerkin Fem

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.

MIXED hp-DISCONTINUOUS GALERKIN FEM FOR LINEAR ELASTICITY AND STOKES FLOW IN THREE DIMENSIONS

2012 ◽  
Vol 22 (08) ◽  
pp. 1250016 ◽  
Author(s):  
THOMAS P. WIHLER ◽  
MARCEL WIRZ
Keyword(s):  
Discontinuous Galerkin ◽  
Linear Elasticity ◽  
Degrees Of Freedom ◽  
Poisson Ratio ◽  
A Priori ◽  
Three Dimensions ◽  
Singular Solutions ◽  
Hexahedral Elements ◽  
Discontinuous Galerkin Fem ◽  
Stability Results

We consider mixed hp-discontinuous Galerkin FEM for linear elasticity in polyhedral domains Ω ⊂ ℝ3. In order to resolve possible corner, edge, and corner–edge singularities, anisotropic axiparallel geometric edge meshes consisting of hexahedral elements are applied. We show inf–sup stability results on both the continuous and the discrete level which are robust with respect to the Poisson ratio as it tends to the incompressible limit of ½. Furthermore, in the subsequent a priori error analysis we derive a quasi-optimality result, including the case of singular solutions. In addition, under certain realistic assumptions (for analytic data) on the regularity of the exact solution, we prove that the proposed DG schemes converge at an exponential rate in terms of the fifth root of the number of degrees of freedom.

Sign in / Sign up

Export Citation Format

Share Document