Maximum-norm a posteriori error estimates for singularly perturbed reaction-diffusion problems on anisotropic meshes

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Abstract

Residual-type a posteriori error estimates in the maximum norm are given for singularly perturbed semilinear reaction-diffusion equations posed in polygonal domains. Linear finite elements are considered on anisotropic triangulations. The error constants are independent of the diameters and the aspect ratios of mesh elements and of the small perturbation parameter.

Original languageEnglish
Pages (from-to)2519-2544
Number of pages26
JournalSIAM Journal on Numerical Analysis
Volume53
Issue number6
DOIs
Publication statusPublished - 2015

Keywords

  • A posteriori error estimate
  • Anisotropic triangulation
  • Maximum norm
  • Reaction-diffusion
  • Singular perturbation

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