A Finite Element Method for Surface Diffusion: the Parametric Case - Bänsch, Eberhard; Morin, Pedro; Nochetto, Ricardo (Journal of Computational Physics, 2005)
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.
UnivIS-Import:2015-03-09:Pub.2005.nat.dma.lama3.afinit
Keywords: Finite elements; Fourth-order parabolic problem; Pinch-off; Schur complement; Smoothing effect; Surface diffusion