Record number :
Title of article :
A finite element method for surface diffusion: the parametric case
Author/Authors :
Bنnsch، نويسنده , , Eberhard and Morin، نويسنده , , Pedro and Nochetto، نويسنده , , Ricardo H.، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2005
Pages :
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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.
Keywords :
surface diffusion , Schur Complement , smoothing effect , Pinch-off , Finite elements , Fourth-order parabolic problem
Journal title :
Journal of Computational Physics
Journal title :
Journal of Computational Physics
Serial Year :
Link To Document :