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Stabilization arising from PGEM: a review and further developments

Araya, R. and Barrenechea, G.R. and Leopoldo, P.F and Valentin, F. (2009) Stabilization arising from PGEM: a review and further developments. Applied Numerical Mathematics, 59 (9). pp. 2065-2081. ISSN 0168-9274

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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.