Cut finite element methods for convection-diffusion problems on time dependent domains

Sara Zahedi
Numerical Analysis Group
Department of Mathematics


I will present a cut finite element method for time dependent convection-diffusion equations on evolving domains. The cut finite element spaces are constructed by first embedding the time-dependent domain in a fixed background grid equipped with a standard finite element space and then taking the restriction of the finite element functions to the domain. The method is optimal order accurate and based on a space-time approach with continuous linear elements in space and discontinuous linear elements in time. To ensure well posedness of the resulting algebraic system of equations we add consistent stabilization terms. This method can be used for simulations of coupled bulk-surface problems such as the evolution of surfactant concentrations.