A framework for obtaining guaranteed error bounds for finite elements approximations

M. Ainsworth

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

We give an overview of our recent progress in developing a framework for the derivation of fully computable guaranteed posteriori error bounds for finite element approximation including conforming, non-conforming, mixed and discontinuous finite element schemes. Whilst the details of the actual estimator are rather different for each particular scheme, there is nonetheless a common underlying structure at work in all cases. We aim to illustrate this structure by treating conforming, non-conforming and discontinuous finite element schemes in a single framework. In taking a rather general viewpoint, some of the finer details of the analysis that rely on the specific properties of each particular scheme are obscured but, in return, we hope to allow the reader to 'see the wood despite the trees'.
Original languageEnglish
Pages (from-to)2618-2632
Number of pages14
JournalJournal of Computational and Applied Mathematics
Volume234
Issue number9
DOIs
Publication statusPublished - 2010

Keywords

  • posteriori error estimation
  • discontinuous Galerkin method
  • guaranteed error bounds
  • finite element analysis

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