Numerical methods for anisotropic mean curvature flow based on a discrete time variational formulation

A fully discrete numerical scheme for weighted mean curvature flow

We analyze a fully discrete numerical scheme approximating the evolution of n–dimensional graphs under anisotropic mean curvature. The highly nonlinear problem is discretized by piecewise linear finite elements in space and semi–implicitly in time. The scheme is unconditionally stable und we obtain optimal error estimates in natural norms. We also present numerical examples which confirm our th...

Anisotropic and Crystalline Mean Curvature Flow

Discrete anisotropic curvature flow of graphs

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A Nested Variational Time Discretization for Parametric Anisotropic Willmore Flow

A variational time discretization of anisotropic Willmore flow combined with a spatial discretization via piecewise affine finite elements is presented. Here, both the energy and the metric underlying the gradient flow are anisotropic, which in particular ensures that Wulff shapes are invariant up to scaling under the gradient flow. In each time step of the gradient flow a nested optimization p...

A Variational Formulation for a Level Set Representation of Multiphase Flow and Area Preserving Curvature Flow∗

Abstract. Variational descriptions for various multiphase level set formulations involving curvature flow are discussed. A representation of n phases using n−1 level set functions is introduced having the advantage that constraints preventing overlaps or vacuum are not needed. The representation is then used in conjunction with our variational formulation to deduce a novel level set based algor...