Mathematisches Kolloquium

The next talk in the mathematical colloquium will take place Friday, 18th of June 2021, 2:15 pm via Zoom (passcode: 186837).

Title: Space-time discretization methods
Speaker: Prof. Olaf Steinbach (University of Graz) hosted by Prof. Dr. Rjasanow
For the numerical solution of time-dependent partial dierential equations we apply space-time discretization methods which are based on a variational formulation in the space-time domain. This approach allows an adaptive resolution of the solution in space and time simultaneously, and parallelization in space and time for an ecient iterative solution. We first discuss a standard space-time variational formulation in Bochner spaces, with applications to the solution of distributed optimal control and inverse problems, subject to the heat equation. More recent work is on time-varying computational domains in order to do a shape optimization of electrical machines.
An alternative approach is a space-time variational formulation in anisotropic Sobolev spaces, where we use a modied Hilbert transformation to end up with a stable scheme in the space-time domain.
This approach also allows to consider the acoustic wave equation, where we present first results for an unconditionally stable space-time nite element method, and new coercivity estimates for related space-time boundary element methods.

The talk is based on joint work with U. Langer (Linz), F. Tröltzsch (Berlin), H. Yang
(Korneuburg), P. Gangl, (Graz), M. Gobrial (Graz), M. Zank (Wien), C. Urzua-Torres
(Delft), and R. Löscher (Darmstadt).