Discontinuous Galerkin error estimation for linear symmetrizable hyperbolic systems

Slimane Adjerid, Thomas Weinhart

Research output: Contribution to journalArticleAcademicpeer-review

18 Citations (Scopus)

Abstract

We present an a posteriori error analysis for the discontinuous Galerkin discretization error of first-order linear symmetrizable hyperbolic systems of partial differential equations with smooth solutions. We perform a local error analysis by writing the local error as a series and showing that its leading term can be expressed as a linear combination of Legendre polynomials of degree and . We apply these asymptotic results to show that projections of the error are pointwise -superconvergent. We solve relatively small local problems to compute efficient and asymptotically exact estimates of the finite element error. We present computational results for several linear hyperbolic systems in acoustics and electromagnetism.
Original languageEnglish
Pages (from-to)1335-1367
JournalMathematics of computation
Volume198
Issue number275
DOIs
Publication statusPublished - 2011

Keywords

  • IR-89621
  • METIS-301981

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