Algorithms for computing motion by mean curvature. (English) Zbl 0863.65061

Walkington, Noel J.

SIAM J. Numer. Anal. 33, No. 6, 2215-2238 (1996).

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.

Reviewer: J.D.P.Donnelly (Oxford)

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

Keywords:

motion by mean curvature; surface motion; stability; numerical examples; finite element algorithm; Brakke flows