Computable error bounds for nonconfirming Fortin-Soulie finite element approximation of the Stokes problem

Mark Ainsworth, Alejandro Ignacio Allendes Flores, Gabriel Barrenechea, Richard Andrew Robert Rankin

Research output: Contribution to journalArticle

  • 3 Citations

Abstract

We propose computable a posteriori error estimates for a second order nonconforming finite element approximation of the Stokes problem. The estimator is completely free of unknown constants and gives a guaranteed numerical upper bound on the error, in terms of a lower bound for the inf-sup constant of the underlying continuous problem. The estimator is also shown to provide a lower bound on the error up to a constant and higher order data oscillation terms. Numerical results are presented illustrating the theory and the performance of the
estimator.
LanguageEnglish
Pages414-447
Number of pages34
JournalIMA Journal of Numerical Analysis
Volume32
Issue number2
DOIs
StatePublished - 2012

Fingerprint

Stokes Problem
Finite Element Approximation
Error Bounds
Estimator
Lower bound
Nonconforming Finite Element
A Posteriori Error Estimates
Oscillation
Higher Order
Upper bound
Unknown
Numerical Results
Term

Keywords

  • a posteriori error estimation
  • Fortin-Soulie element
  • nonconforming finite element

Cite this

Ainsworth, Mark ; Allendes Flores, Alejandro Ignacio ; Barrenechea, Gabriel ; Rankin, Richard Andrew Robert. / Computable error bounds for nonconfirming Fortin-Soulie finite element approximation of the Stokes problem. In: IMA Journal of Numerical Analysis . 2012 ; Vol. 32, No. 2. pp. 414-447
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Computable error bounds for nonconfirming Fortin-Soulie finite element approximation of the Stokes problem. / Ainsworth, Mark; Allendes Flores, Alejandro Ignacio; Barrenechea, Gabriel; Rankin, Richard Andrew Robert.

In: IMA Journal of Numerical Analysis , Vol. 32, No. 2, 2012, p. 414-447.

Research output: Contribution to journalArticle

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