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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 StammWe 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.
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Publication status
- Published
Journal
SIAM Journal on Numerical AnalysisISSN
0036-1429External DOI
Issue
1Volume
47Page range
508-533Pages
26.0Department affiliated with
- Mathematics Publications
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- No
Peer reviewed?
- Yes
Legacy Posted Date
2012-02-06Usage metrics
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