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

Time: Thu 2022-02-10 14.00 - 15.00

Location: Zoom

Video link: Meeting ID: 632 9929 3349

Participating: Simon Sticko (Uppsala University)

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.