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Low order discontinuous Galerkin methods for 2nd order elliptic problems

journal contribution
posted on 2023-06-08, 07:18 authored by E Burman, B Stamm
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.

History

Publication status

  • Published

Journal

SIAM Journal on Numerical Analysis

ISSN

0036-1429

Issue

1

Volume

47

Page range

508-533

Pages

26.0

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2012-02-06

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