A supercloseness result for the discontinuous Galerkin stabilization of convection-diffusion problems on Shishkin Meshes

Hans Görg Roos, Helena Zarin

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20 Scopus citations

Abstract

We consider a convection-diffusion problem with Dirichlet boundary conditions posed on a unit square. The problem is discretized using a combination of the standard Galerkin FEM and an h-version of the non-symmetric discontinuous Galerkin FEM with interior penalties on a layer-adapted mesh with linear/bilinear elements. With specially chosen penalty parameters for edges from the coarse part of the mesh, we prove uniform convergence (in the perturbation parameter) in an associated norm. In the same norm we also establish a supercloseness result. Numerical tests support our theoretical estimates.

Original languageEnglish (US)
Pages (from-to)1560-1576
Number of pages17
JournalNumerical Methods for Partial Differential Equations
Volume23
Issue number6
DOIs
StatePublished - Nov 1 2007
Externally publishedYes

Keywords

  • Convection-diffusion problem
  • Finite element method
  • Interior penalty
  • Layer-adapted mesh
  • Singular perturbation
  • Superconvergence

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