Finite element approximation of reaction–diffusion problems using an exponentially graded mesh

Research output: Contribution to journalResearch articleContributedpeer-review

Contributors

Abstract

We present the analysis of an [Formula presented] version Finite Element Method for the approximation of the solution to singularly perturbed reaction–diffusion problems posed in smooth domains [Formula presented]. The method uses piecewise polynomials of degree [Formula presented] in each variable, defined on an exponentially graded mesh, optimally constructed for the approximation of exponential layers. We establish robust, optimal convergence rates in a variety of norms and illustrate our theoretical findings through numerical computations.

Details

Original languageEnglish
Pages (from-to)2523-2534
Number of pages12
JournalComputers and Mathematics with Applications
Volume76
Issue number10
Publication statusPublished - 15 Nov 2018
Peer-reviewedYes

External IDs

ORCID /0000-0002-2458-1597/work/142239734

Keywords

Keywords

  • Balanced norm, Boundary layers, Exponential mesh, Reaction–diffusion, Uniform optimal convergence