Stabilization arising from PGEM: a review and further developments

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

Research output: Contribution to journalArticle

9 Citations (Scopus)

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.
LanguageEnglish
Pages2065-2081
Number of pages16
JournalApplied Numerical Mathematics
Volume59
Issue number9
DOIs
Publication statusPublished - Sep 2009

Fingerprint

Stabilized Finite Element Method
Petrov-Galerkin
Singularly Perturbed Problem
Stokes Problem
Mixed Problem
Galerkin methods
Condensation
Stabilization
Numerical Solution
Finite element method
Form
Review

Keywords

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

Cite this

Araya, Rodolfo ; Barrenechea, Gabriel R. ; Franca, Leopoldo P. ; Valentin, Frédéric. / Stabilization arising from PGEM : a review and further developments. In: Applied Numerical Mathematics. 2009 ; Vol. 59, No. 9. pp. 2065-2081.
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Stabilization arising from PGEM : a review and further developments. / Araya, Rodolfo; Barrenechea, Gabriel R.; Franca, Leopoldo P. ; Valentin, Frédéric.

In: Applied Numerical Mathematics, Vol. 59, No. 9, 09.2009, p. 2065-2081.

Research output: Contribution to journalArticle

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