Discontinuous Galerkin error estimation for hyperbolic problems on unstructured triangular meshes

Mahboub Baccouch, Slimane Adjerid

Research output: Contribution to journalArticle

26 Scopus citations

Abstract

We extend the error analysis of Adjerid and Baccouch [1,2] for the discontinuous Galerkin discretization error to variable-coefficient linear hyperbolic problems as well as nonlinear hyperbolic problems on unstructured meshes. We further extend this analysis to transient hyperbolic problems and prove that the local superconvergence results presented in [1] still hold for both steady and transient variable-coefficient linear and nonlinear problems. This local error analysis allows us to construct asymptotically correct a posteriori error estimates by solving local hyperbolic problems with no boundary conditions on each element of general unstructured meshes. We illustrate the superconvergence and the efficiency of our a posteriori error estimates by showing computational results for several linear and nonlinear numerical examples.

Original languageEnglish (US)
Pages (from-to)162-177
Number of pages16
JournalComputer Methods in Applied Mechanics and Engineering
Volume200
Issue number1-4
DOIs
StatePublished - Jan 1 2011

Keywords

  • A posteriori error estimation
  • Discontinuous Galerkin method
  • Hyperbolic problems
  • Superconvergence
  • Transient convection problems
  • Unstructured meshes

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications

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