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An algorithm for mean curvature motion. (English) Zbl 1061.35147
Author’s abstract: We propose in this paper a new algorithm for computing the evolution by mean curvature of a hypersurface. Our algorithm is a variant of the variational approach of F. Almgren, J. E. Taylor and L.-H. Wang [SIAM J. Control Optim. 31, No. 2, 387–438 (1993; Zbl 0783.35002)]. We show that it approximates, as the time-step goes to zero, the generalized motion (in the sense of barriers or viscosity solutions). The results still hold for the anisotropic mean curvature motion, as long as the anisotropy is smooth.

MSC:
35K55 Nonlinear parabolic equations
53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010)
35A35 Theoretical approximation in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
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