Numerical Aspects of Density Driven Flow in Porous Media

The analysis as well as the numerical simulation of density driven flow in porous media is still a challenging task. Whereas thorough theoretical investigations are limited to special situations, the numerical treatment, especially of real-world problems, requires special numerical techniques. In this talk we focus on two aspects, which are relevant in this context. The first deals with the design of robust multigrid solvers for problems with high spatial anisotropies. In the second part, we investigate the structure of the steady state solutions for a special model problem. The results shed some light on the the difficulties arising in the analysis of the underlying mathematical problem.