ABSTRACT

In the talk I will present recent results on how to design and analyse hypocoercivity-preserving Galerkin discretisations, in an effort to port the concept of hypocoercivity in the design and analysis of cutting-edge numerical methods. To that end I plan to start by presenting the first provably hypocoercivity-preserving Galerkin (non-conforming) finite element method for the model problem of Kolmogorov equation and discuss some very recent results on a different approach for the same equation. I plan to conclude with some first results of Galerkin methods for the inhomogeneous  Fokker-Plack equation on exponentially weighted function spaces. The results are joint work with E. H. Georgoulis (Heriot-Watt University & National Technical University of Athens) and Philip Herbert (University of Sussex).