Consistency result for a non monotone scheme for anisotropic mean curvature flow
نویسندگان
چکیده
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). We analyse the resulting scheme, following the work of Ishii-Pires-Souganidis on the convergence of the Bence-Merriman-Osher algorithm for isotropic motion by mean curvature. The main difficulty here, is that the kernel Kφ,t is not positive and that its moments of order 2 are not in L1(Rd). Still, we can show that in one sense the scheme is consistent with the anisotropic mean curvature flow.
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