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An area-minimizing scheme for anisotropic mean-curvature flow. (English) Zbl 1275.35014

The authors prove the convergence of an area-minimizing scheme for anisotropic mean curvature flow that originally due to A. Chambolle [Interfaces Free Bound. 6, No. 2, 195–218 (2004; Zbl 1061.35147)] in the sense of Hausdorff distance by the level set method provided that no flattening occurs. This an area-minimizing scheme is related to the area-minimizing scheme introduced by Almgren-Taylor-Wang [F. Almgren et al., SIAM J. Control Optimization 31, No. 2, 387–438 (1993; Zbl 0783.35002)].

MSC:

35A35 Theoretical approximation in context of PDEs
35K65 Degenerate parabolic equations
53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010)
35D40 Viscosity solutions to PDEs
35K67 Singular parabolic equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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