WIAS Preprint No. 805, (2003)
Finite element methods for surface diffusion
Authors
- Bänsch, Eberhard
ORCID: 0000-0003-2743-1612 - Morin, Pedro
- Nochetto, Ricardo H.
2010 Mathematics Subject Classification
- 35K55 65M12 65M15 65M60 65Z05
Keywords
- Surface diffusion, fourth-order parabolic problem, finite elements, a priori error estimates, Schur complement, smooth ing effect, pinch-off
DOI
Abstract
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.
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