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Fully discrete finite element approximation for anisotropic surface diffusion of graphs. (English) Zbl 1094.65098

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.

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
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