Summary
An Algorithm is presented which allows to split the calculation of the mean curvature flow of surfaces with or without boundary into a series of Poisson problems on a series of surfaces. This gives a new method to solve Plateau's problem forH-surfaces.
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References
[B] Brakke, K.A.: the motion of a surface by its mean curvature. Math. Notes, Princeton Univ. Press, Princeton N.J., 1978
[D] Dziuk, G.: Finite elements for the Beltrami operator on arbitrary surfaces. In: S. Hildebrandt, R. Leis (ed.) Partial differential equations and calculus of variations. Lect. Notes Math Vol. 1357, pp. 142–155, Berlin Heidelberg New York: Springer 1988
[H1] Huisken, G.: Flow by mean curvature of convex surfaces into spheres. J. Diff. Geom.20, 237–266 (1984)
[H2] Huisken, G.: Non-parametric mean curvature evolution with boundary conditions. CMA Research Report 44 (1987)
[H3] Huisken, G.: Asymptotic behaviour for singularities of the mean curvature flow. CMA Research Report 49 (1987)
[W] Wohlrab, O.: Zur numerischen Behandlung von parametrischen Minimalflächen mit halbfreien Rändern. Dissertation Bonn 1989
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Dziuk, G. An algorithm for evolutionary surfaces. Numer. Math. 58, 603–611 (1990). https://doi.org/10.1007/BF01385643
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DOI: https://doi.org/10.1007/BF01385643