Bänsch E, Morin P, Nochetto R (2005)
Publication Type: Journal article, Original article
Publication year: 2005
Publisher: Elsevier
Book Volume: 203
Pages Range: 321-343
Journal Issue: 1
DOI: 10.1016/j.jcp.2004.08.022
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. © 2004 Elsevier Inc. All rights reserved.
APA:
Bänsch, E., Morin, P., & Nochetto, R. (2005). A Finite Element Method for Surface Diffusion: the Parametric Case. Journal of Computational Physics, 203(1), 321-343. https://doi.org/10.1016/j.jcp.2004.08.022
MLA:
Bänsch, Eberhard, Pedro Morin, and Ricardo Nochetto. "A Finite Element Method for Surface Diffusion: the Parametric Case." Journal of Computational Physics 203.1 (2005): 321-343.
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