The discontinuous Galerkin method for two-dimensional hyperbolic problems. Part I: Superconvergence error analysis

Slimane Adjerid, Mahboub Baccouch

Research output: Contribution to journalArticle

40 Scopus citations

Abstract

In this paper we investigate the superconvergence properties of the discontinuous Galerkin method applied to scalar first-order hyperbolic partial differential equations on triangular meshes. We show that the discontinuous finite element solution is O(h p+2) superconvergent at the Legendre points on the outflow edge for triangles having one outflow edge. For triangles having two outflow edges the finite element error is O(h p+2) superconvergent at the end points of the inflow edge. Several numerical simulations are performed to validate the theory. In Part II of this work we explicitly write down a basis for the leading term of the error and construct asymptotically correct a posteriori error estimates by solving local hyperbolic problems with no boundary conditions on more general meshes.

Original languageEnglish (US)
Pages (from-to)75-113
Number of pages39
JournalJournal of Scientific Computing
Volume33
Issue number1
DOIs
StatePublished - Oct 1 2007

Keywords

  • Discontinuous Galerkin method
  • Hyperbolic problems
  • Superconvergence
  • Triangular meshes

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

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