Simon Sticko: High-Order CutFEM with BDF on Time-Dependent Domains

Abstract: We consider fully discrete methods for solving the advection-diffusion equation on time-dependent domains. These methods use the high-order stabilized cut finite element method as spatial discretization and backward difference formulas (BDF) for time-stepping. We consider both the case when the domain is a d-dimensional bounded subset of \(\mathbb{R}^d\) and when it is a \((d-1)\)-dimensional manifold. We focus on combining Lagrange elements of order p with BDF of order \(p+1\), with \(p<5\). We show numerical experiments to investigate the order of convergence. For some test cases, we observe optimal order: \(p+1\), while for others suboptimal.