An approximation scheme for the anisotropic and nonlocal mean curvature flow

In 2004 Chambolle proposed an algorithm for mean curvature flow based on a variational problem. Since then, the convergence, extensions and applications of his algorithm have been studied by many people. In this paper we give a proof of the convergence of an anisotropic version of Chambolle’s algorithm by use of the signed distance function. An application of our scheme to an approximation of the nonlocal curvature flow such as crystalline one is also discussed.