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

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

Authors

Emmanuil H. Georgoulis Emmanuil.Georgoulis@mcs.le.ac.uk

Edward Hall Edward.Hall@nottingham.ac.uk

Jens Markus Melenk melenk@tuwien.ac.ut



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.

Journal Article Type Article
Publication Date Jan 1, 2009
Journal Journal of Scientific Computing
Print ISSN 0885-7474
Electronic ISSN 0885-7474
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
APA6 Citation Georgoulis, E. H., Hall, E., & Melenk, J. M. (2009). On the suboptimality of the p-version interior penalty discontinuous Galerkin method. Journal of Scientific Computing,
Keywords discontinuous Galerkin method, interior penalty, a priori error estimation, p-version, suboptimality.
Publisher URL http://www.springerlink.com/content/g075179366551117/fulltext.pdf
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf
Additional Information The original publication is available at www.springerlink.com

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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