Numerische Mathematik

, Volume 74, Issue 3, pp 261–282

Anisotropic mesh refinement in stabilized Galerkin methods

  • Thomas Apel
  • Gert Lube

DOI: 10.1007/s002110050216

Cite this article as:
Apel, T. & Lube, G. Numer. Math. (1996) 74: 261. doi:10.1007/s002110050216

Summary.

The numerical solution of a convection-diffusion-reaction model problem is considered in two and three dimensions. A stabilized finite element method of Galerkin/Least-square type accomodates diffusion-dominated as well as convection- and/or reaction-dominated situations. The resolution of boundary layers occuring in the singularly perturbed case is achieved using anisotropic mesh refinement in boundary layer regions. In this paper, the standard analysis of the stabilized Galerkin method on isotropic meshes is extended to more general meshes with boundary layer refinement. Simplicial Lagrangian elements of arbitrary order are used.

Mathematics Subject Classification (1991):65N30, 65N50 

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Thomas Apel
    • 1
  • Gert Lube
    • 2
  1. 1.Technische Universität Chemnitz-Zwickau, Fakultät für Mathematik, D–09107 Chemnitz, Germany; email: na.apel@na-net.ornl.gov DE
  2. 2.Georg-August-Universtät Göttingen, Fachbereich Mathematik, Institut für Numerische und Angewandte Mathematik, Lotzestrasse 16–18, D–37083 Göttingen, Germany; email: lube@namu01.gwdg.de DE

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