Discontinuous Galerkin Methods for Second-Order Elliptic PDE with Low-Regularity Solutions

Authors:
Thomas P. Wihler;Béatrice Rivière
Affiliations:
Mathematics Institute, University of Bern, Bern, Switzerland 3012;Computational and Applied Mathematics Department, Rice University, Houston, USA TX 77005-1892
Venue:
Journal of Scientific Computing
Year:
2011

Citing 7
Cited 2

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Finite Element Method for Elliptic Problems
Discontinuous hp-Finite Element Methods for Advection-Diffusion-Reaction Problems

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A Priori Error Estimates for Finite Element Methods Based on Discontinuous Approximation Spaces for Elliptic Problems

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Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems

SIAM Journal on Numerical Analysis
An A Priori Error Analysis of the Local Discontinuous Galerkin Method for Elliptic Problems

SIAM Journal on Numerical Analysis
Discontinuous Galerkin Methods For Solving Elliptic And parabolic Equations: Theory and Implementation

Discontinuous Galerkin Methods For Solving Elliptic And parabolic Equations: Theory and Implementation
Numerical Approximation of Partial Differential Equations

Numerical Approximation of Partial Differential Equations

Convergence of the discontinuous finite volume method for elliptic problems with minimal regularity

Journal of Computational and Applied Mathematics
A Posteriori Error Estimates of Discontinuous Galerkin Method for Nonmonotone Quasi-linear Elliptic Problems

Journal of Scientific Computing

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Abstract

In this paper we derive an a priori error analysis for interior penalty discontinuous Galerkin finite element discretizations of the Poisson equation with exact solution in W 2,p , p驴(1,2]. We show that the DGFEM converges at an optimal algebraic rate with respect to the number of degrees of freedom.