Deckelnick, Klaus; Dziuk, Gerhard; Elliott, Charles M. Fully discrete finite element approximation for anisotropic surface diffusion of graphs. (English) Zbl 1094.65098 SIAM J. Numer. Anal. 43, No. 3, 1112-1138 (2005). The authors analyze a fully discrete numerical scheme for approximating the evolution of graphs for surfaces evolving by anisotropic surface diffusion. The scheme is based on the idea of a second order operator splitting for a nonlinear geometric fourth order equation. The authors prove error bounds for the resulting scheme and also present numerical test calculations that confirm their analysis and illustrate the surface diffusion. Reviewer: Răzvan Răducanu (Iaşi) Cited in 14 Documents MSC: 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 35K55 Nonlinear parabolic equations 65M15 Error bounds for initial value and initial-boundary value problems involving PDEs Keywords:surface diffusion; anisotropic; geometric motion; second order operator splitting; finite element; error estimates; fourth order parabolic equation; numerical examples PDFBibTeX XMLCite \textit{K. Deckelnick} et al., SIAM J. Numer. Anal. 43, No. 3, 1112--1138 (2005; Zbl 1094.65098) Full Text: DOI