Discontinuous Galerkin error estimation for linear symmetric hyperbolic systems

Slimane Adjerid, Thomas Weinhart

Research output: Contribution to journalArticleAcademic

22 Citations (Scopus)

Abstract

In this manuscript we present an error analysis for the discontinuous Galerkin discretization error of multi-dimensional first-order linear symmetric hyperbolic systems of partial differential equations. 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 p and p+1p+1. We apply these asymptotic results and 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 one, two and three dimensions.
Original languageEnglish
Pages (from-to)3113-3129
Number of pages17
JournalComputer methods in applied mechanics and engineering
Volume198
Issue number37-40
DOIs
Publication statusPublished - 2009
Externally publishedYes

Keywords

  • Discontinuous Galerkin methods
  • Linear hyperbolic systems
  • A posteriori error estimation
  • Superconvergence

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