Computable error bounds for finite element approximation on nonpolygonal domains

Mark Ainsworth, Richard Rankin

Research output: Journal PublicationArticlepeer-review

1 Citation (Scopus)

Abstract

We consider the case of piecewise affine approximation of the solution to the Poisson problem, with pure Neumann boundary data, on nonpolygonal domains. A computable, guaranteed upper bound on the energy norm of the error in such a finite element approximation is obtained. The estimator takes the effect of the boundary approximation into account and provides, up to a constant and oscillation terms, local lower bounds on the energy norm of the error.

Original languageEnglish
Pages (from-to)604-645
Number of pages42
JournalIMA Journal of Numerical Analysis
Volume37
Issue number2
DOIs
Publication statusPublished - 1 Apr 2017
Externally publishedYes

Keywords

  • computable error bounds
  • finite element approximation
  • nonpolygonal domains.

ASJC Scopus subject areas

  • Mathematics (all)
  • Computational Mathematics
  • Applied Mathematics

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