Finite Element Methods for Surface Diffusion

Abstract

Surface diffusion is a (4th order highly nonlinear) geometric driven motion of a surface with normal velocity proportional to the surface Laplacian of the mean curvature. We present a novel variational formulation for the parametric case, develop a finite element method, and propose a Schur complement approach to solve the resulting linear systems. We also introduce a new graph formulation and state an optimal a priori error estimate. We conclude with several significant simulations, some with pinch-off in finite time.