Pointwise approximation of corner singularities for a singularly perturbed reaction-diffusion equation in an L-shaped domain

Vladimir B. Andreev, Natalia Kopteva

Research output: Contribution to journalArticlepeer-review

Abstract

A singularly perturbed reaction-diffusion equation is posed in a two-dimensional L-shaped domain Ω subject to a continuous Dirchlet boundary condition. Its solutions are in the Holder space C2/3 (ω̄) and typically exhibit boundary layers and corner singularities. The problem is discretized on a tensor-product Shishkin mesh that is further refined in a neighboorhood of the vertex of angle 37π/2. We establish almost second-order convergence of our numerical method in the discrete maximum norm, uniformly in the small diffusion parameter. Numerical results are presented that support our theoretical error estimate.

Original languageEnglish
Pages (from-to)2125-2139
Number of pages15
JournalMathematics of Computation
Volume77
Issue number264
DOIs
Publication statusPublished - Oct 2008

Keywords

  • Corner singularity
  • L-shaped domain
  • Pointwise error estimate
  • Reaction-diffusion
  • Second order
  • Shishkin mesh
  • Singular perturbation

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