GEOMETRICALLY HIGHER ORDER UNFITTED SPACE-TIME METHODS FOR PDEs ON MOVING DOMAINS

In this paper, we propose new geometrically unfitted space-time finite element methods for partial differential equations posed on moving domains of higher order accuracy in space and time. As a model problem, the convection-diffusion problem on a moving domain is studied. For geometrically higher order accuracy, we apply a parametric mapping on a background space-time tensor-product mesh. Concerning discretization in time, we consider discontinuous Galerkin, as well as related continuous (Petrov-)Galerkin and Galerkin collocation methods. For stabilization with respect to bad cut configurations and as an extension mechanism that is required for the latter two schemes, a ghost penalty stabilization is employed. The article puts an emphasis on the techniques that allow us to achieve a robust but higher order geometry handling for smooth domains. We investigate the computational properties of the respective methods in a series of numerical experiments. These include studies in different dimensions for different polynomial degrees in space and time, validating the higher order accuracy in both variables.