Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



$ hp$-Optimal discontinuous Galerkin methods for linear elliptic problems

Authors: Benjamin Stamm and Thomas P. Wihler
Journal: Math. Comp. 79 (2010), 2117-2133
MSC (2010): Primary 65N30
Published electronically: April 9, 2010
MathSciNet review: 2684358
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2010): 65N30

Retrieve articles in all journals with MSC (2010): 65N30

Additional Information

Benjamin Stamm
Affiliation: Division of Applied Mathematics, Brown University, 182 George Street, Box F, Providence, RI 02912

Thomas P. Wihler
Affiliation: Mathematics Institute, University of Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland

Keywords: $hp$-methods, discontinuous Galerkin methods, optimal error estimates.
Received by editor(s): October 26, 2007
Received by editor(s) in revised form: June 20, 2009
Published electronically: April 9, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.