Maximum norm a posteriori error estimate for a 2d singularly perturbed semilinear reaction-diffusion problem

Natalia Kopteva

Research output: Contribution to journalArticle

22 Citations (Scopus)
144 Downloads (Pure)

Abstract

A singularly perturbed semilinear reaction-diffusion equation, posed in the unit square, is discretized on arbitrary nonuniform tensor-product meshes. We establish a second-order maximum norm a posteriori error estimate that holds true uniformly in the small diffusion parameter. No mesh aspect ratio assumption is made. Numerical results are presented that support our theoretical estimate


Original languageEnglish
Pages (from-to)1602-1618
Number of pages17
JournalSIAM Journal on Numerical Analysis
Volume46
Issue number3
DOIs
Publication statusPublished - 2008

Keywords

  • reaction-diffusion
  • singular perturbation
  • a posteriori error estimate
  • maximum norm
  • no mesh aspect ratio condition
  • finite differences
  • layer-adapted mesh

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