03-33
Fully discrete semi-implicit second order splitting for anisotropic surface diffusion of graphs
by Deckelnick, K.; Dziuk, G.; Elliott, C.M.
Preprint series: 03-33, Preprints
- MSC:
- 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
- 35K55 Nonlinear PDE of parabolic type
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
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