Published: Jan. 26, 2024

Gunilla Kreiss, Department of Information Technology, Uppsala University

Cut FEM meets finite differences

There is a cut-FEM methodology with ghost penalty stabilization, which can be applied to hyperbolic conservation laws and wave equations, and allows for using Cartesian grids. Explicit time-stepping is preferable for hyperbolic problems. The stabilization will ensure stability and time-step restrictions similar to the corresponding standard method on the Cartesian grid. However, the standard DG and CG metods suffer from increasingly severe time-step restrictions as the order of the method increases. For high order finite difference methods the time-step restriction is not at all as severe. In this talk we will explore possibilities of applying the cut-FEM methodology to finite difference methods. The goal is to formulate a finite difference method that can be seen as a Galerkin method. Applying the cut-FEM methodology will then yield a finite difference method, which accommodates immersed boundaries.

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