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Minimal Stabilization for Discontinuous Galerkin Finite Element Methods for Hyperbolic Problems

Burman, E. ; Stamm, B.

In: Journal of Scientific Computing, 2007, vol. 33, no. 2, p. 183-208

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    Titre
    • Minimal Stabilization for Discontinuous Galerkin Finite Element Methods for Hyperbolic Problems
    Auteur
    • Burman, E.. Institute of Analysis and Scientific Computing, Swiss Institute of Technology, 1015, Lausanne, Switzerland
    • Stamm, B.. Institute of Analysis and Scientific Computing, Swiss Institute of Technology, 1015, Lausanne, Switzerland
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Journal of Scientific Computing, 2007, vol. 33, no. 2, p. 183-208. Springer US; http://www.springer-ny.com
    Autre version électronique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:320092
    Summary
    We consider a discontinuous Galerkin finite element method for the advection-reaction equation in two space-dimensions. For polynomial approximation spaces of degree greater than or equal to two on triangles we propose a method where stability is obtained by a penalization of only the upper portion of the polynomial spectrum of the jump of the solution over element edges. We prove stability in the standard h-weighted graphnorm and obtain optimal order error estimates with respect to mesh-size