Abstract for the talk at 07.06.2001 (15:00 h)

Arnold Reusken (RWTH Aachen)

On Grad-Div stabilization of Stokes equations

We consider the stationary Stokes equations with a small parameter in front of the diffusion term. If we use standard LBB stable finite element spaces for the discretization of this problem the constants in the discretization errors blow up if the diffusion parameter tends to zero. This instability is observed in numerical experiments, too. It is known from the literature that the problem can be stabilized by using a so-called grad-div stabilization. We explain the idea behind this technique and present a theoretical analysis which shows why this method indeed has a stabilizing effect.