Maximum norm a posteriori error estimates for a 1D singularly perturbed semilinear reaction-diffusion problem

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Abstract

A singularly perturbed semilinear two-point boundary-value problem is discretized on arbitrary non-uniform meshes. We present second-order maximum norm a posteriori error estimates that hold true uniformly in the small parameter. Their application to monitor-function equidistribution and a posteriori mesh refinement are discussed. Numerical results are presented that support our theoretical estimates.

Original languageEnglish
Pages (from-to)576-592
Number of pages17
JournalIMA Journal of Numerical Analysis
Volume27
Issue number3
DOIs
Publication statusPublished - Jul 2007

Keywords

  • A posteriori error estimate
  • Finite differences
  • Grid equidistribution
  • Layer-adapted mesh
  • Maximum norm
  • Reaction-diffusion
  • Singular perturbation

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