On the suboptimality of the p-version interior penalty discontinuous Galerkin method

Georgoulis, Emmanuil H.; Hall, Edward; Melenk, Jens Markus

Abstract

We address the question of the rates of convergence of the p-version interior penalty discontinuous Galerkin method (p-IPDG) for second order elliptic problems with non-homogeneous Dirichlet boundary conditions. It is known that the p-IPDG method admits slightly suboptimal a-priori bounds with respect to the polynomial degree (in the Hilbertian Sobolev space setting). An example for which the
suboptimal rate of convergence with respect to the polynomial degree is both proven theoretically and
validated in practice through numerical experiments is presented. Moreover, the performance of p-
IPDG on the related problem of p-approximation of corner singularities is assessed both theoretically and numerically, witnessing an almost doubling of the convergence rate of the p-IPDG method.

Citation

Georgoulis, E. H., Hall, E., & Melenk, J. M. On the suboptimality of the p-version interior penalty discontinuous Galerkin method. Journal of Scientific Computing,

• Journal Article Type: Article
• Deposit Date: Sep 21, 2009
• Publicly Available Date: Sep 21, 2009
• Journal: Journal of Scientific Computing
• Print ISSN: 0885-7474
• Electronic ISSN: 1573-7691
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Keywords: discontinuous Galerkin method, interior penalty, a priori error estimation, p-version, suboptimality.
• Public URL: https://nottingham-repository.worktribe.com/output/1014413
• Publisher URL: http://www.springerlink.com/content/g075179366551117/fulltext.pdf
• Additional Information: The original publication is available at www.springerlink.com