Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
A regularized equation for anisotropic motion-by-curvature
SIAM Journal on Applied Mathematics
Finite element approximation of the Cahn-Hilliard equation with concentration dependent mobility
Mathematics of Computation
Shapes and geometries: analysis, differential calculus, and optimization
Shapes and geometries: analysis, differential calculus, and optimization
Semi-Implicit Level Set Methods for Curvature and Surface Diffusion Motion
Journal of Scientific Computing
A finite element method for surface diffusion: the parametric case
Journal of Computational Physics
Numerical simulation of anisotropic surface diffusion with curvature-dependent energy
Journal of Computational Physics
AMDiS: adaptive multidimensional simulations
Computing and Visualization in Science
A Discrete Scheme for Parametric Anisotropic Surface Diffusion
Journal of Scientific Computing
A level set approach to anisotropic flows with curvature regularization
Journal of Computational Physics
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In this paper we shall discuss the numerical simulation of geometric flows by level set methods. Main examples under considerations are higher order flows, such as surface diffusion and Willmore flow as well as variants of them with more complicated surface energies. Such problems find various applications, e.g. in materials science (thin film growth, grain boundary motion), biophysics (membrane shapes), and computer graphics (surface smoothing and restoration).We shall use spatial discretizations by finite element methods and semi-implicit time stepping based on local variational principles, which allows to maintain dissipation properties of the flows by the discretization. In order to compensate for the missing maximum principle, which is indeed a major hurdle for the application of level set methods to higher order flows, we employ frequent redistancing of the level set function.Finally we also discuss the solution of the arising discretized linear systems in each time step and some particular advantages of the finite element approach such as the variational formulation which allows to handle the higher order and various anisotropies efficiently and the possibility of local adaptivity around the zero level set.