Superconvergence of the local discontinuous Galerkin method for elliptic problems on Cartesian grids

Bernardo Cockburn, Guido Kanschat, Ilaria Perugia, Dominik Schötzau

Research output: Contribution to journalArticle

189 Scopus citations

Abstract

In this paper, we present a superconvergence result for the local discontinuous Galerkin (LDG) method for a model elliptic problem on Cartesian grids. We identify a special numerical flux for which the L2-norm of the gradient and the L2-norm of the potential are of orders k + 1/2 and k + 1, respectively, when tensor product polynomials of degree at most k are used; for arbitrary meshes, this special LDG method gives only the orders of convergence of k and k + 1/2, respectively. We present a series of numerical examples which establish the sharpness of our theoretical results.

Original languageEnglish (US)
Pages (from-to)264-285
Number of pages22
JournalSIAM Journal on Numerical Analysis
Volume39
Issue number1
DOIs
StatePublished - Dec 1 2002

Keywords

  • Cartesian grids
  • Discontinuous Galerkin methods
  • Elliptic problems
  • Finite elements
  • Superconvergence

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