Numerical simulation of anisotropic surface diffusion with curvature-dependent energy

The aim of this paper is the numerical simulation of surface diffusion processes in the presence of a strong anisotropy and curvature dependence in the surface energy. We derive semi-implicit finite element discretizations based on a splitting into three second-order equations. The discretization we use yields indefinite linear systems for the nodal values of the height function, the curvature concentration, and the chemical potential. We provide several numerical examples and parametric studies with respect to some of the parameters in the surface energy and with respect to the coverage. The results, to our knowledge the first that have been obtained for this model, confirm theoretical predictions, namely partial faceting of the surfaces with rounded corners.