Relationship between multiscale enrichment and stabilized finite element methods for the generalized Stokes problem

We derive a new stabilized finite element method for the generalized Stokes problem starting from the non-stable continuous ${\mathbb{P}}_1/{\mathbb{P}}_1$ finite element space enriched with multiscale functions. The stabilization parameter is related with the enrichment functions which are analytically computed from a boundary value problem at the element level leading to a method which is free of constants. Optimal error estimates are obtained in natural norms and numerical tests validate the method. To cite this article: G.R. Barrenechea, F. Valentin, C. R. Acad. Sci. Paris, Ser. I 341 (2005).