Prof. Dr. Thomas Wick, Leibniz Universität Hannover

In this presentation, we discuss progress over the last decade in space-time numerical modeling of nonstationary, nonlinear, coupled PDE systems and variational inequality systems (CVIS). Classical coupled problems include for instance the Navier-Stokes equations, fluid-structure interaction, and porous media. Phase-field fracture is an example of a CVIS. We discuss the entire road-map from problem statements given in strong form, over weak formulations, regularization, temporal discretization, spatial discretization, nonlinear solution, up to linear solvers. Moreover, the evaluation of quantities of interest with the help of adjoint-based error-controlled adaptivity is discussed. In addition, these developments can be applied to numerical optimization such as optimal control in which CVIS serve as the so-called forward problem. Finally, in our Hannover-Paris collaboration space-time concepts have been applied to digitial image correlation and digital volume correlation, respectively. Our numerical simulations are substantiated with computational convergence studies, computational cost analyses, and in some cases validation with experimental results in order to study the accuracy, efficiency, and robustness of our methods.