A variational formulation of anisotropic geometric evolution equations in higher dimensions |
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Authors: | John W Barrett Harald Garcke Robert Nürnberg |
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Institution: | 1.Department of Mathematics,Imperial College London,London,UK;2.NWF I, Mathematik,Universit?t Regensburg,Regensburg,Germany |
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Abstract: | We present a novel variational formulation of fully anisotropic motion by surface diffusion and mean curvature flow in , d ≥ 2. This new formulation leads to an unconditionally stable, fully discrete, parametric finite element approximation in
the case d = 2 or 3. The resulting scheme has very good properties with respect to the distribution of mesh points and, if applicable,
volume conservation. This is demonstrated by several numerical experiments for d = 3, including regularized crystalline mean curvature flow and regularized crystalline surface diffusion. |
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Keywords: | 65M60 65M12 35K55 53C44 74E10 74E15 |
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