Numerical approximation of anisotropic geometric evolution equations in the plane

Harald Garcke Naturwissenchaftliche Fakultät I' Mathematik, Universität Regensburg, 93040 Regensburg, Germany Robert Nürnberg Department of Mathematics, Imperial College London, London SW7 2AZ, UK Received on 13 April 2006. Revised on 20 February 2007. We present a variational formulation of fully anisotropic motionby surface diffusion and mean curvature flow, as well as relatedflows. The proposed scheme covers both the closed-curve caseand the case of curves that are connected via triple junctionpoints. On introducing a parametric finite-element approximation,we prove stability bounds and report on numerical experiments,including regularized crystalline mean curvature flow and regularizedcrystalline surface diffusion. The presented scheme has verygood properties with respect to the distribution of mesh pointsand, if applicable, area conservation.