$hp$-Optimal discontinuous Galerkin methods for linear elliptic problems
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- by Benjamin Stamm and Thomas P. Wihler PDF
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Abstract:
The aim of this paper is to present and analyze a class of $hp$-version discontinuous Galerkin (DG) discretizations for the numerical approximation of linear elliptic problems. This class includes a number of well-known DG formulations. We will show that the methods are stable provided that the stability parameters are suitably chosen. Furthermore, on (possibly irregular) quadrilateral meshes, we shall prove that the schemes converge all optimally in the energy norm with respect to both the local element sizes and polynomial degrees provided that homogeneous boundary conditions are considered.References
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Additional Information
- Benjamin Stamm
- Affiliation: Division of Applied Mathematics, Brown University, 182 George Street, Box F, Providence, RI 02912
- MR Author ID: 824171
- ORCID: 0000-0003-3375-483X
- Email: Benjamin_Stamm@Brown.edu
- Thomas P. Wihler
- Affiliation: Mathematics Institute, University of Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland
- MR Author ID: 662940
- ORCID: 0000-0003-1232-0637
- Email: wihler@math.unibe.ch
- Received by editor(s): October 26, 2007
- Received by editor(s) in revised form: June 20, 2009
- Published electronically: April 9, 2010
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 79 (2010), 2117-2133
- MSC (2010): Primary 65N30
- DOI: https://doi.org/10.1090/S0025-5718-10-02335-5
- MathSciNet review: 2684358