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.
- Stokes operator
- reactive flow
- multiscale function
- Petrov-Galerkin method
Araya, R., Barrenechea, G. R., Franca, L. P., & Valentin, F. (2009). Stabilization arising from PGEM: a review and further developments. Applied Numerical Mathematics, 59(9), 2065-2081. https://doi.org/10.1016/j.apnum.2008.12.004