Uniform pointwise convergence of difference schemes for convection-diffusion problems on layer-adapted meshes

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Abstract

We consider two convection-diffusion boundary value problems in conservative form: for an ordinary differential equation and for a parabolic equation. Both the problems are discretized using a four-point second-order upwind space difference operator on arbitrary and layer-adapted space meshes. We give ε-uniform maximum norm error estimates O(N-2ln2N(+τ)) and O(N-2(+τ)), respectively, for the Shishkin and Bakhvalov space meshes, where N is the space meshnodes number, τ is the time mesh-interval. The smoothness condition for the Bakhvalov mesh is replaced by a weaker condition.

Original languageEnglish
Pages (from-to)179-197
Number of pages19
JournalComputing (Vienna/New York)
Volume66
Issue number2
DOIs
Publication statusPublished - 2001

Keywords

  • Bakhvalov mesh
  • Convection-diffusion problems
  • Four-point upwind difference scheme
  • Shishkin mesh
  • Singular perturbation

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