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A finite element method for surface diffusion:: the parametric case
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DOI：10.1016/j.jcp.2004.08.022.png)
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Abstract
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Surface diffusion is a (fourth 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 parametric surfaces with or without boundaries. The method is semi-implicit, requires no explicit parametrization, and yields a linear system of elliptic PDE to solve at each time step. We next develop a finite element method, propose a Schur complement approach to solve the resulting linear systems, and show several significant simulations, some with pinch-off in finite time. We introduce a mesh regularization algorithm, which helps prevent mesh distortion, and discuss the use of time and space adaptivity to increase accuracy while reducing complexity. (C) 2004 Elsevier Inc. All rights reserved.
Keywords:
surface diffusion
fourth-order parabolic problem
finite elements
Schur complement
smoothing effect
pinch-off
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