Geometrically Higher Order Unfitted Space-Time Methods for PDEs on Moving Domains
Fabian Heimann, Christoph Lehrenfeld, Janosch Preuß
Abstract
In this paper, we propose new geometrically unfitted space-time Finite \nElement methods for partial differential equations posed on moving domains of \nhigher order accuracy in space and time. As a model problem, the \nconvection-diffusion problem on a moving domain is studied. For geometrically \nhigher order accuracy, we apply a parametric mapping on a background space-time \ntensor-product mesh. Concerning discretisation in time, we consider \ndiscontinuous Galerkin, as well as related continuous (Petrov-)Galerkin and \nGalerkin collocation methods. For stabilisation with respect to bad cut \nconfigurations and as an extension mechanism that is required for the latter \ntwo schemes, a ghost penalty stabilisation is employed. The article puts an \nemphasis on the techniques that allow to achieve a robust but higher order \ngeometry handling for smooth domains. We investigate the computational \nproperties of the respective methods in a series of numerical experiments. \nThese include studies in different dimensions for different polynomial degrees \nin space and time, validating the higher order accuracy in both variables.