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The Discontinuous Galerkin Finite Element Method for Singularly Perturbed Problems

  • Hans-Görg Roos
  • Helena Zarin
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 35)

Abstract

A nonsymmetric discontinuous Galerkin finite element method with interior penalties is considered for two—dimensional singularly perturbed problems. On an anisotropic Shishkin mesh with bilinear elements we prove error estimates (uniformly in the perturbation parameter) in an integral norm associated with this method. We perform separate analyses for the cases of reaction—diffusion and convection—diffusion problems. On different types of interelement edges we derive the values of discontinuity—penalization parameters. Numerical experiments support the theoretical results.

Keywords

Finite Element Method Perturbation Parameter Discontinuous Galerkin Method Finite Element Space Interior Penalty 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Hans-Görg Roos
    • 1
  • Helena Zarin
    • 2
  1. 1.Institut für Numerische MathematikTechnische Universität DresdenDresdenGermany
  2. 2.Institute of Mathematics, Faculty of ScienceUniversity of Novi SadNovi SadYugoslavia

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