An adaptive stabilized finite element method for the generalized Stokes problem

Rodolfo Araya, Gabriel R. Barrenechea, Abner Poza

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Abstract

In this work we present an adaptive strategy (based on an a posteriori error estimator) for a stabilized finite element method for the Stokes problem, with and without a reaction term. The hierarchical type estimator is based on the solution of local problems posed on appropriate finite dimensional spaces of bubble-like functions. An equivalence result between the norm of the finite element error and the estimator is given, where the dependence of the constants on the physics of the problem is explicited. Several numerical results confirming both the theoretical results and the good performance of the estimator are given.
Original languageEnglish
Pages (from-to)457-479
Number of pages22
JournalJournal of Computational and Applied Mathematics
Volume214
Issue number2
DOIs
Publication statusPublished - 1 May 2008

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Keywords

  • Stokes equation
  • a posteriori error estimator
  • bubble function
  • stabilized finite element method
  • adapted mesh

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