Fully discrete finite element approximation for anisotropic surface diffusion of graphs

摘要

We 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 second order operator splitting for the nonlinear geometric fourth order equation. This yields two coupled spatially 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 numerical test calculations that confirm our analysis and illustrate surface diffusion.