Stable space and time discretization for coupled multi-physics problems

In this talk, we will consider several coupled multi-physics problems from different applications areas such as finance, porous media and continuum mechanics. Quite often the naive application of standard discretization schemes results in poor numerical results and spurious oscillations in time or locking in space can be observed. Many of these problems can be written as constrained minimization problems on a convex set. Due to the inequality character and the non-linearities in the formulation, the numerical simulation is still challenging. Here we address several of these challenges and present a variationally consistent space discretization and an energy preserving stable time integration method. The abstract framework of saddle point problems and local a priori estimates can help to provide optimal error bounds. Numerical results show the flexibility and the robustness.