A numerical scheme for regularized anisotropic curve shortening flow |
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Institution: | Crystal Growth Group, Research Center caesar, Ludwig-Erhard-Allee 2, 53175 Bonn, Germany |
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Abstract: | Realistic interfacial energy densities are often non-convex, which results in backward parabolic behavior of the corresponding anisotropic curve shortening flow, thereby inducing phenomena such as the formation of corners and facets. Adding a term that is quadratic in the curvature to the interfacial energy yields a regularized evolution equation for the interface, which is fourth-order parabolic. Using a semi-implicit time discretization, we present a variational formulation of this equation, which allows the use of linear finite elements. The resulting linear system is shown to be uniquely solvable. We also present numerical examples. |
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