Sara Zahedi: Cut Finite Element Methods for multiphase flow problems

Abstract: I will present so called Cut Finite Element Methods (Cut FEM) for simulations of multiphase flow phenomena. In particular, I will present a Cut FEM for convection diffusion problems on a given time dependent surface, modeling the evolution of a surfactant. The cut finite element method is constructed by embedding the surface in a background grid and then using the restriction to the surface of a finite element space defined on the background grid. The surface is allowed to cut through the background grid in an arbitrary fashion, i.e. the interface does not need to conform to the mesh. To ensure well posedness of the resulting algebraic systems of equations, independent of the position of the surface in the background grid, we add a consistent stabilization term. I will discuss both a Cut FEM based on a characteristic-Galerkin formulation and a Cut FEM based on a space-time formulation.