Relationship between multiscale enrichment and stabilized finite element methods for the generalized Stokes problem
Gabriel R. Barrenechea, Frédéric Valentin · Comptes Rendus Mathématique · 2005
We derive a new stabilized finite element method for the generalized Stokes problem starting from the non-stable continuous P 1 / 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.