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Algorithms for computing motion by mean curvature. (English) Zbl 0863.65061
The author proposes a finite element algorithm for computing the motion of a surface whose motion is governed by its mean curvature. The algorithm is based on level sets. Stability is proved in \(L^\infty\) and \(W^{1,1}\) and existence is deduced. A connection with Brakke flows is shown. Numerical examples are given.

MSC:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35K70 Ultraparabolic equations, pseudoparabolic equations, etc.
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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