Finite element methods for surface diffusion
- Bänsch, Eberhard
- Morin, Pedro
- Nochetto, Ricardo H.
2010 Mathematics Subject Classification
- 35K55 65M12 65M15 65M60 65Z05
- Surface diffusion, fourth-order parabolic problem, finite elements, a priori error estimates, Schur complement, smooth ing effect, pinch-off
Surface diffusion is a (4th order highly nonlinear) geometric driven motion of a surface with normal velocity proportional to the surface Laplacian of 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.