Discrete quadratic curvature energies
ACM SIGGRAPH 2006 Courses
A parametric finite element method for fourth order geometric evolution equations
Journal of Computational Physics
Higher-Order Feature-Preserving Geometric Regularization
SIAM Journal on Imaging Sciences
Level Set Based Multispectral Segmentation with Corners
SIAM Journal on Imaging Sciences
Journal of Scientific Computing
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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.