Subgrid stabilization of galerkin approximations of linear contraction semi-groups of class C-O in Hilbert spaces

This article presents a stabilized Galerkin technique for approximating ii near contraction semi-groups of class C-0 in a Hilbert space. The main resu lt of this article is that this technique yields an optimal approximation e stimate in the graph norm. The key idea is two-fold. First, it consists in introducing an approximation space that is broken up into resolved scales a nd subgrid scales, so that the bilinear form associated with the generator of the semi-group satisfies a uniform inf-sup condition with respect to thi s decomposition. Second, the Galerkin approximation is slightly modified by introducing an artificial diffusion on the subgrid scales. Numerical tests show that the method applies also to nonlinear semi-groups. (C) 2001 John Wiley & Sons, Inc.