620 RWTH Publication No: 976529        2024       
TITLE Analysis of a space-time unfitted finite element method for PDEs on evolving surfaces
AUTHORS Arnold Reusken, Hauke Sass
ABSTRACT In this paper we analyze a space-time unfitted finite element method for the discretization of scalar surface partial differential equations on evolving surfaces. For higher order approximations of the evolving surface we use the technique of (iso)parametric mappings for which a level set representation of the evolving surface is essential. We derive basic results in which certain geometric characteristics of the exact space-time surface are related to corresponding ones of the numerical surface approximation. These results are used in a complete error analysis of a higher order space-time TraceFEM.
KEYWORDS surface partial differential equation, space-time finite element method, CutFEM, TraceFEM, finite element error analysis