Robust a posteriori error estimation for the nonconforming fortin-soulie finite element approximation

M. Ainsworth, R. Rankin

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

We obtain a computable a posteriori error bound on the broken energy norm of the error in the Fortin-Soulie finite element approximation of a linear second order elliptic problem with variable permeability. This bound 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. The estimator is completely free of unknown constants and provides a guaranteed numerical bound on the error.
LanguageEnglish
Pages1917-1939
Number of pages22
JournalMathematics of Computation
Volume77
Issue number264
DOIs
Publication statusPublished - 2008

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A Posteriori Error Estimation
Finite Element Approximation
Error analysis
Norm
Second-order Elliptic Problems
Linear Order
Energy
Permeability
Error Bounds
Oscillation
Higher Order
Lower bound
Estimator
Unknown
Term

Keywords

  • robust a posteriori error estimation
  • nonconforming finite element
  • fortin-Soulie element

Cite this

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Robust a posteriori error estimation for the nonconforming fortin-soulie finite element approximation. / Ainsworth, M.; Rankin, R.

In: Mathematics of Computation, Vol. 77, No. 264, 2008, p. 1917-1939.

Research output: Contribution to journalArticle

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AU - Rankin, R.

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AB - We obtain a computable a posteriori error bound on the broken energy norm of the error in the Fortin-Soulie finite element approximation of a linear second order elliptic problem with variable permeability. This bound 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. The estimator is completely free of unknown constants and provides a guaranteed numerical bound on the error.

KW - robust a posteriori error estimation

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