A finite element method for surface diffusion: the parametric case

Authors:
Eberhard Bänsch;Pedro Morin;Ricardo H. Nochetto
Affiliations:
Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin, Germany and Freie Universität Berlin, Germany;Instituto de Matemática Aplicada del Litoral (IMAL) and Departamento de Matemática, Facultad de Ingeniería Química, Universidad Nacional del Litoral, Güemes 3450, 3000 San ...;Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA
Venue:
Journal of Computational Physics
Year:
2005

Citing 2
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Abstract

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.