Stabilization arising from PGEM: A review and further developments

Autores: Rodolfo Araya, Gabriel R. Barrenechea , Leopoldo P. Franca, Frédéric Valentin
Localización: Applied numerical mathematics, ISSN-e 0168-9274, Vol. 59, Nº. 9, 2009, págs. 2065-2081
Idioma: inglés
DOI: 10.1016/j.apnum.2008.12.004
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Resumen
- 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.