An algorithm for evolutionary surfaces. (English) Zbl 0714.65092

Using the finite element method in space coordinates and then an implicit time discretization in time t, the author presents a numerical algorithm to evaluate the mean curvature flow of surfaces with or without boundary which are described in time by the equation \(\partial u/\partial t- \Delta_{S(t)}u=2 H(u)n,\quad u(,0)=u_ 0,\) where \(\Delta_{S(t)}\) is the Beltrami operator on S(t), H being the mean curvature of S(t). As a limit case as \(t\to \infty\), this method can give a solution to Plateau’s problem for H-surfaces. Some numerical results and their graphic pictures are also presented.
Reviewer: L.P.Lebedev


65Z05 Applications to the sciences
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35Q80 Applications of PDE in areas other than physics (MSC2000)
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
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