On the motion of a phase interface by surface diffusion
Zeitschrift für Angewandte Mathematik und Physik (ZAMP)
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
A level set approach to anisotropic flows with curvature regularization
Journal of Computational Physics
Finite Element-Based Level Set Methods for Higher Order Flows
Journal of Scientific Computing
Higher-Order Feature-Preserving Geometric Regularization
SIAM Journal on Imaging Sciences
Level Set Based Multispectral Segmentation with Corners
SIAM Journal on Imaging Sciences
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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.