Space-time unfitted finite element methods for time-dependent problems on moving domains

Abstract

We propose a space-time scheme that combines an unfitted finite element method in space with a discontinuous Galerkin time discretisation for the accurate numerical approximation of parabolic problems with moving domains or interfaces. We make use of an aggregated finite element space to attain robustness with respect to the cut locations. The aggregation is performed slab-wise to have a tensor product structure of the space-time discrete space, which is required in the numerical analysis. As an alternative, we also propose a space-time ghost penalty stabilisation term to attain robustness. We analyse the proposed algorithm, providing stability, condition number bounds and anisotropic a priori error estimates. A set of numerical experiments confirm the theoretical results for a parabolic problem on a moving domain. The method is applied for a mass transfer problem with changing topology.