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Numerical approximation of gradient flows for closed curves in Rd

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Barrett, John W. ; Garcke, Harald ; Nürnberg, Robert
Date of publication of this fulltext: 24 Mar 2010 06:26


We present parametric finite element approximations of curvature flows for curves in Rd, d ≥ 2, as well as for curves on two-dimensional manifolds in R3. Here we consider the curve shortening flow, curve diffusion and the elastic flow. It is demonstrated that the curve shortening and the elastic flows on manifolds can be used to compute nontrivial geodesics, and that the corresponding geodesic ...


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