Resumen de Stabilization arising from PGEM: A review and further developments

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

• 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.