A finite element method for surface diffusion: the parametric case

By E. Bänsch, Pedro Morin, Ricardo H. Nochetto. 2005

152 citations recorded by the source corpus.

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.

Subfields: Computational Mechanics, Fluid Flow and Transfer Processes, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/5972180ae3c8fb6741deda1873cb0d5e462e0c49

Citations in the corpus

• The approximation of planar curve evolutions by stable fully implicit finite element schemes that equidistribute (2011, unknown): “[7, 8, 15] for possible mesh smoothing strategies.”