Stabilization arising from PGEM: a review and further developments

Rodolfo Araya, Gabriel R. Barrenechea, Leopoldo P. Franca, Frédéric Valentin

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9 Citations (Scopus)
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Abstract

The aim of this paper is twofold. First, we review the recent Petrov-Galerkin enriched method (PGEM) to stabilize numerical solutions of BVP's in primal and mixed forms. Then, we extend such enrichment technique to a mixed singularly perturbed problem, namely, the generalized Stokes problem, and focus on a stabilized finite element method arising in a natural way after performing static condensation. The resulting stabilized method is shown to lead to optimal convergences, and afterward, it is numerically validated.
Original languageEnglish
Pages (from-to)2065-2081
Number of pages16
JournalApplied Numerical Mathematics
Volume59
Issue number9
DOIs
Publication statusPublished - Sep 2009

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Keywords

  • Stokes operator
  • reactive flow
  • multiscale function
  • Petrov-Galerkin method
  • stabilization

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