Stabilization arising from PGEM: a review and further developments

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

doi:10.1016/j.apnum.2008.12.004

Stabilization arising from PGEM: a review and further developments

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

Mathematics And Statistics

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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 language	English
Pages (from-to)	2065-2081
Number of pages	16
Journal	Applied Numerical Mathematics
Volume	59
Issue number	9
DOIs	https://doi.org/10.1016/j.apnum.2008.12.004
Publication status	Published - Sept 2009

Keywords

Stokes operator
reactive flow
multiscale function
Petrov-Galerkin method
stabilization

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title = "Stabilization arising from PGEM: a review and further developments",

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.",

keywords = "Stokes operator, reactive flow, multiscale function, Petrov-Galerkin method, stabilization",

author = "Rodolfo Araya and Barrenechea, {Gabriel R.} and Franca, {Leopoldo P.} and Fr{\'e}d{\'e}ric Valentin",

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AU - Araya, Rodolfo

AU - Barrenechea, Gabriel R.

AU - Franca, Leopoldo P.

AU - Valentin, Frédéric

PY - 2009/9

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N2 - 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.

AB - 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.

KW - Stokes operator

KW - reactive flow

KW - multiscale function

KW - Petrov-Galerkin method

KW - stabilization

U2 - 10.1016/j.apnum.2008.12.004

DO - 10.1016/j.apnum.2008.12.004

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JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

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ER -

Stabilization arising from PGEM: a review and further developments

Abstract

Keywords

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