POINTWISE A POSTERIORI ERROR ESTIMATES FOR DISCONTINUOUS GALERKIN METHODS FOR SINGULARLY PERTURBED REACTION-DIFFUSION EQUATIONS*

Natalia Kopteva, Richard Rankin

Research output: Contribution to journalArticlepeer-review

Abstract

The symmetric interior penalty discontinuous Galerkin method and its version with weighted averages are considered on shape-regular nonconforming meshes with an arbitrarily large number of mesh faces contained in any element face. For this method, residual-type a posteriori error estimates in the maximum norm are given for singularly perturbed semilinear reaction-diffusion equations posed in polyhedral domains. The error constants are independent of the diameters of mesh elements and of the small perturbation parameter. The theoretical findings are illustrated by numerical experiments.

Original languageEnglish
Pages (from-to)1938-1961
Number of pages24
JournalSIAM Journal on Numerical Analysis
Volume61
Issue number4
DOIs
Publication statusPublished - 2023

Keywords

  • a posteriori error estimate
  • discontinuous Galerkin method
  • maximum norm
  • reaction-diffusion
  • singular perturbation

Fingerprint

Dive into the research topics of 'POINTWISE A POSTERIORI ERROR ESTIMATES FOR DISCONTINUOUS GALERKIN METHODS FOR SINGULARLY PERTURBED REACTION-DIFFUSION EQUATIONS*'. Together they form a unique fingerprint.

Cite this