Higher Order Unfitted Space-Time Methods for Transport Problems

Abstract: In this article, we present an Unfitted Space-Time Finite Element method for the scalar transport equation posed on moving domains. We consider the case of the domain boundary being transported by the same velocity field as the scalar concentration inside the physical domain. A standard continuous Galerkin Finite element space is considered on a fixed background mesh, as well as tensor product Space-Time elements, which can be discontinuous along time slice boundaries. For the computational geometry, we opt for a spatially second-order accurate approximation variant in the mathematical analysis. In particular, we establish stability in a problem-specific norm and prove a priori error bounds of high order. Numerical examples illustrate these theoretical findings.