WS, Fabian Heimann: Higher Order Unfitted Space-Time Finite Element Methods

Speaker
Fabian Heimann,University College London

Abstract
In recent years, the framework of Unfitted Finite Element Methods was developed in order to facilitate the handling of complex geometries in Finite Element simulations. We build on these results and present the application of space-time methods to solve moving domain problems. In particular, an isoparametric mapping is generalised in space and time to yield computationally feasible discrete geometries. We start by presenting numerical results of convergence of an arbitrary high order of the proposed method, first at the example of a moving domain convection-diffusion bulk problem. Next, we review the rigorous mathematical proof of this property, involving both a geometry and a discretisation error analysis. Finally, we present the application of these computational tools to a coupled surface-bulk convection-diffusion problem and the transport equation.