Zurück zu den Preprints des Jahres 2003


2003-33

Fully discrete semi-implicit second order splitting for anisotropic surface diffusion of graphs

by Deckelnick, K., Dziuk, G., Elliott, C.M..


Series: 2003-33, Preprints

MSC:
65N30 Finite elements, ~Rayleigh-Ritz and Galerkin methods, finite methods
35K55 Nonlinear parabolic equations

Abstract:
We analyze a fully discrete numerical scheme for approximating the
evolution of graphs for surfaces evolving by anisotropic surface
diffusion. The nonlinear geometric fourth order equation is split
into two coupled second order problems, which are approximated
by linear finite elements. The time-discretization is semi-implicit.
We prove error bounds for the resulting scheme and present test
calculations that confirm our analysis and illustrate surface
diffusion.

Keywords:
Surface diffusion, anisotropic, geometric motion, fully discrete, error estimates, fourth order parabolic PDE