| Título: | A finite element method for surface diffusion: the parametric case |
| Autores: |
Pedro Morin; IMAL-CONICET-UNL Eberhard Bänsch Ricardo H. Nochetto |
| Fecha: | 2006-08-12 |
| Publicador: | Cuadernos de Matemática y Mecánica |
| Fuente: |
 |
| Tipo: |
Articles |
| Tema: | No aplica |
| Descripción: | Abstract: Surface diffusion is a (4th 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, fourth-order parabolic problem, finite elements, Schur complement, smoothing effect, pinch-off. AMS Subject Classifications: 35K55, 65M12, 65M15, 65M60, 65Z05. Published: Journal of Computational Physics 203 (2005) 321--343. Published: Journal of Computational Physics 203 (2005) 321--343. |
| Idioma: | Inglés |
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