Speaker
Olaf Steinbach, TU Graz
Abstract
In this talk we consider new space-time finite element formulations for a stable and efficient numerical solution of the Stokes system. While the momentum equation is first order in time, the continuity equation for an incompressible fluid does not cover any time derivative. However, the ansatz space for the velocity implies some regularity in time also for the pressure. A first space-time variational formulation, which turns out to be equivalent to the Crank-Nicolson scheme, shows some mismatch in the used function spaces. We will discuss two different approaches to correct these differences. This approach can be extended not only to the Navier-Stokes system, but also to more general parabolic-elliptic or parabolic-hyperbolic problems.