Optimal a priori error estimates for the hp-version of the local discontinuous Galerkin method for convection-diffusion problems

Paul Castillo, Bernardo Cockburn, Dominik Schötzau, Christoph Schwab

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151 Scopus citations

Abstract

We study the convergence properties of the hp-version of the local discontinuous Galerkin finite element method for convection-diffusion problems; we consider a model problem in a one-dimensional space domain. We allow arbitrary meshes and polynomial degree distributions and obtain upper bounds for the energy norm of the error which are explicit in the mesh-width h, in the polynomial degree p, and in the regularity of the exact solution. We identify a special numerical flux for which the estimates are optimal in both h and p. The theoretical results are confirmed in a series of numerical examples.

Original languageEnglish (US)
Pages (from-to)455-478
Number of pages24
JournalMathematics of Computation
Volume71
Issue number238
DOIs
StatePublished - 2002

Keywords

  • Convection-diffusion
  • Discontinious Galerkin methods
  • hp-methods

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