Consistency result for a non monotone scheme for anisotropic mean curvature flow

Consistency result for a non monotone scheme for anisotropic mean curvature flow

In this paper, we propose a new scheme for anisotropic motion by mean curvature in R. The scheme consists of a phase-field approximation of the motion, where the nonlinear diffusive terms in the corresponding anisotropic Allen-Cahn equation are linearized in the Fourier space. In real space, this corresponds to the convolution with a specific kernel of the form Kφ,t(x) = F−1 [ e−4π 2tφo(ξ) ] (x...

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

Singularities of Lagrangian Mean Curvature Flow: Monotone Case

We study the formation of singularities for the mean curvature flow of monotone Lagrangians in C. More precisely, we show that if singularities happen before a critical time then the tangent flow can be decomposed into a finite union of area-minimizing Lagrangian cones (Slag cones). When n = 2, we can improve this result by showing that connected components of the rescaled flow converge to an a...

Mean Curvature Blowup in Mean Curvature Flow

In this note we establish that finite-time singularities of the mean curvature flow of compact Riemannian submanifolds M t →֒ (N, h) are characterised by the blow up of the mean curvature.