WIAS Preprint No. 805, (2003)

Finite element methods for surface diffusion



Authors

  • Bänsch, Eberhard
  • 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

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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