Stabilization arising from PGEM : a review and further developments

Araya, Rodolfo and Barrenechea, Gabriel R. and Franca, Leopoldo P. and Valentin, Frédéric (2009) Stabilization arising from PGEM : a review and further developments. Applied Numerical Mathematics, 59 (9). pp. 2065-2081. ISSN 0168-9274 (https://doi.org/10.1016/j.apnum.2008.12.004)

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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.

ORCID iDs

Araya, Rodolfo, Barrenechea, Gabriel R. ORCID logoORCID: https://orcid.org/0000-0003-4490-678X, Franca, Leopoldo P. and Valentin, Frédéric;
CORE (COnnecting REpositories)