A second-order scheme for singularly perturbed differential equations with discontinuous source term

H. G. Roos, H. Zarin

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

A Galerkin finite element method that uses piecewise linear functions on Shishkin- and Bakhvalov-Shishkin-type of meshes is applied to a linear reaction-diffusion equation with discontinuous source term. The method is shown to be convergent, uniformly in the perturbation parameter, of order N-2ln2N for the Shishkin-type mesh and N-2 for the Bakhvalov-Shishkin-type mesh, where N is the mesh size number. Numerical experiments support our theoretical results.

Original languageEnglish (US)
Pages (from-to)275-289
Number of pages15
JournalJournal of Numerical Mathematics
Volume10
Issue number4
DOIs
StatePublished - 2002
Externally publishedYes

Bibliographical note

Funding Information:
Institute of Numerical Mathematics, Technical University, D-01062 Dresden, Germany †Institute of Mathematics, Faculty of Science, University of Novi Sad, 21000 Novi Sad, Yugoslavia This paper was written during a visit to the Technical University of Dresden in June-December 2001 supported by DAAD grant.

Keywords

  • Finite element method
  • Reaction-diffusion problems
  • Shishkin mesh
  • Singular perturbation

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