Asymptotically exact a posteriori error estimates for a one-dimensional linear hyperbolic problem

Slimane Adjerid, Mahboub Baccouch

Research output: Contribution to journalArticle

32 Scopus citations

Abstract

In this manuscript we investigate the global convergence of the implicit residual-based a posteriori error estimates of Adjerid et al. (2002) [3]. The authors used the discontinuous Galerkin method to solve one-dimensional transient hyperbolic problems and showed that the local error on each element is proportional to a Radau polynomial. The discontinuous Galerkin error estimates under investigation are computed by solving a local steady problem on each element. Here we prove that, for smooth solutions, these a posteriori error estimates at a fixed time t converge to the true spatial error in the L2 norm under mesh refinement.

Original languageEnglish (US)
Pages (from-to)903-914
Number of pages12
JournalApplied Numerical Mathematics
Volume60
Issue number9
DOIs
StatePublished - Sep 1 2010

Keywords

  • A posteriori error estimation
  • Discontinuous Galerkin
  • Hyperbolic problems

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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