Discretization Error Analysis of a High Order Unfitted Space-Time Method for moving domain problems

Abstract: We present a numerical analysis of a higher order unfitted space-time Finite Element method applied to a convection-diffusion model problem posed on a moving bulk domain. The method uses isoparametric space-time mappings for the geometry approximation of level set domains and has been presented and investigated computationally in [Heimann, Lehrenfeld, Preu{\ss}, SIAM J. Sci. Comp. 45(2), 2023, B139 - B165]. Recently, in [Heimann, Lehrenfeld, IMA J. Numer. Anal., 2025] error bounds for the geometry approximation have been proven. In this paper we prove stability and accuracy including the influence of the geometry approximation.