Picture water droplets

Developing mathematical theories of the physical world: Open Access research on fluid dynamics from Strathclyde

Strathprints makes available Open Access scholarly outputs by Strathclyde's Department of Mathematics & Statistics, where continuum mechanics and industrial mathematics is a specialism. Such research seeks to understand fluid dynamics, among many other related areas such as liquid crystals and droplet evaporation.

The Department of Mathematics & Statistics also demonstrates expertise in population modelling & epidemiology, stochastic analysis, applied analysis and scientific computing. Access world leading mathematical and statistical Open Access research!

Explore all Strathclyde Open Access research...

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

[img]
Preview
PDF (abfv-apnum-revised.pdf)
abfv-apnum-revised.pdf
Accepted Author Manuscript

Download (1MB) | Preview

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.