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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Letzte Änderung: 01.03.2018 - Ansprechpartner: Webmaster