hp-FEM for reaction–diffusion equations. II: robust exponential convergence for multiple length scales in corner domains

Lehel Banjai, Jens M. Melenk, Christoph Schwab

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

In bounded, polygonal domains Ω⊂R2 with Lipschitz boundary ∂Ω consisting of a finite number of Jordan curves admitting analytic parametrizations, we analyze hp-FEM discretizations of linear, second-order, singularly perturbed reaction–diffusion equations on so-called geometric boundary layer meshes. We prove, under suitable analyticity assumptions on the data, that these hp-FEM afford exponential convergence in the natural ‘energy’ norm of the problem, as long as the geometric boundary layer mesh can resolve the smallest length scale present in the problem. Numerical experiments confirm the robust exponential convergence of the proposed hp-FEM.
Original languageEnglish
Pages (from-to)3282-3325
Number of pages44
JournalIMA Journal of Numerical Analysis
Volume43
Issue number6
Early online date6 Dec 2022
DOIs
Publication statusPublished - Nov 2023

Keywords

  • anisotropic hp-refinement
  • exponential convergence
  • geometric corner refinement

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics
  • Mathematics(all)

Fingerprint

Dive into the research topics of 'hp-FEM for reaction–diffusion equations. II: robust exponential convergence for multiple length scales in corner domains'. Together they form a unique fingerprint.

Cite this