Eulerian Finite Element Methods for Parabolic Equations on Moving Surfaces

Abstract

Three new Eulerian finite element methods for parabolic PDEs on a moving surface $\Gamma(t)$ are presented and compared in numerical experiments. These are space-time Galerkin methods, which are derived from a weak formulation in space and time. The trial- and test-spaces contain the traces on the space-time manifold of an outer prismatic finite element space. The numerical experiments show that two of the methods converge with second order with respect to both the time step size and the spatial mesh width.