Low order discontinuous Galerkin methods for 2nd order elliptic problems

Burman, E and Stamm, B (2008) Low order discontinuous Galerkin methods for 2nd order elliptic problems. SIAM Journal on Numerical Analysis, 47 (1). pp. 508-533. ISSN 0036-1429

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We consider DG-methods for second order scalar elliptic problems using piecewise affine approximation in two or three space dimensions. We prove that both the symmetric and the nonsymmetric versions of the DG-method have regular system matrices without penalization of the interelement solution jumps provided boundary conditions are imposed in a certain weak manner. Optimal convergence is proved for sufficiently regular meshes and data. We then propose a DG-method using piecewise affine functions enriched with quadratic bubbles. Using this space we prove optimal convergence in the energy norm for both a symmetric and nonsymmetric DG-method without stabilization. All of these proposed methods share the feature that they conserve mass locally independent of the penalty parameter.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Erik Burman
Date Deposited: 06 Feb 2012 20:40
Last Modified: 11 Apr 2012 08:01
URI: http://sro.sussex.ac.uk/id/eprint/27416
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