On the stability of bubble functions and a stabilized mixed finite element formulation for the Stokes problem

Abstract

In this paper we investigate the relationship between stabilized and enriched finite element formulations for the Stokes problem. We also present a new stabilized mixed formulation for which the stability parameter is derived purely by the method of weighted residuals. This new formulation allows equal order interpolation for the velocity and pressure fields. Finally, we show by counterexample that a direct equivalence between subgrid-based stabilized finite element methods and Galerkin methods enriched by bubble functions cannot be constructed for quadrilateral and hexahedral elements using standard bubble functions.Comment: 25 pages, 13 figures (The previous version was compiled by mistake with the wrong style file, the current one uses amsart, and there is no difference in the text or the figures