Fully computable bounds for the error in nonconforming finite element approximations of arbitrary order on triangular elements

Mark Ainsworth, Richard Rankin

Research output: Journal PublicationArticlepeer-review

21 Citations (Scopus)

Abstract

We obtain a fully computable a posteriori error bound on the broken energy norm of the error in the nonconforming finite element approximation on triangles of arbitrary order of a linear second order elliptic problem with variable permeability. The estimator is completely free of unknown constants and provides a guaranteed numerical bound on the broken energy norm of the error. This estimator is shown to be efficient in the sense that it also provides a lower bound for the broken energy norm of the error up to a constant and higher order data oscillation terms.

Original languageEnglish
Pages (from-to)3207-3232
Number of pages26
JournalSIAM Journal on Numerical Analysis
Volume46
Issue number6
DOIs
Publication statusPublished - 2008
Externally publishedYes

Keywords

  • Nonconforming finite element
  • Robust a posteriori error estimation

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'Fully computable bounds for the error in nonconforming finite element approximations of arbitrary order on triangular elements'. Together they form a unique fingerprint.

Cite this