Eskil Hansen

The goal of my group's current research is to design and analyze state-of-the-art numerical schemes for partial differential equations (PDEs) that can be cast into the frameworks of nonlinear evolution equations, e.g., the semigroup approach. Such PDEs include degenerate parabolic systems, damped wave equations, infinite dimensional Riccati systems and nonlinear Schrödinger equations.

These PDEs commonly occur in engineering and medical applications, and there is a large demand for highly efficient numerics tailored to the specific applications. Due to the sheer size of these equation systems, the usage of direct approximation methods is not feasible and one needs to partition or split the problem. Schemes based on this splitting strategy often constitute a very competitive method choice, but a thorough understanding of the schemes' convergence behaviors and geometric properties is essential in order to put them to proper use.