Numerical approximation of gradient flows for closed curves in Rd

URN to cite this document:: urn:nbn:de:bvb:355-epub-137991
DOI to cite this document:: 10.5283/epub.13799

Barrett, John W. ; Garcke, Harald ; Nürnberg, Robert

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Date of publication of this fulltext: 24 Mar 2010 06:26

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Abstract

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 ...