A singularly perturbed problem with two parameters on a Bakhvalov-type mesh

Mirjana Brdar, Helena Zarin

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

A singularly perturbed problem with two small parameters is considered. On a Bakhvalov-type mesh we prove uniform convergence of a Galerkin finite element method with piecewise linear functions. Arguments in the error analysis include interpolation error bounds for a Clément quasi-interpolant as well as discretization error estimates in an energy norm. Numerical experiments support theoretical findings.

Original languageEnglish (US)
Pages (from-to)307-319
Number of pages13
JournalJournal of Computational and Applied Mathematics
Volume292
DOIs
StatePublished - Aug 3 2016
Externally publishedYes

Bibliographical note

Funding Information:
The work has been supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia , Projects 174030 and III44006 . The authors would like to thank the anonymous reviewers for their valuable comments and suggestions which improved the quality of the paper.

Publisher Copyright:
© 2015 Elsevier B.V. All rights reserved.

Keywords

  • Bakhvalov-type mesh
  • Clément quasi-interpolant
  • Galerkin finite element method
  • Singularly perturbed problem
  • Two small parameters

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