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

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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.
Original languageEnglish
Pages (from-to)414-447
Number of pages34
JournalIMA Journal of Numerical Analysis
Volume32
Issue number2
DOIs
Publication statusPublished - 2012

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Keywords

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

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