On the Suboptimality of the p-Version Interior Penalty Discontinuous Galerkin Method

  • Emmanuil H. Georgoulis
  • Edward Hall
  • Jens Markus Melenk
Article

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.

Keywords

Discontinuous Galerkin method Interior penalty A priori error estimation p-version Suboptimality 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Emmanuil H. Georgoulis
    • 1
  • Edward Hall
    • 2
  • Jens Markus Melenk
    • 3
  1. 1.Department of MathematicsUniversity of LeicesterLeicesterUK
  2. 2.School of Mathematical SciencesUniversity of NottinghamNottinghamUK
  3. 3.Institut für Analysis und Scientific ComputingTechnische Universität WienViennaAustria

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