Simon Sticko
Division of Scientific Computing, IT Department, Uppsala University
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 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 cases, we observe optimal order: p+1, while for others suboptimal.