# Discrete gradient flows for general curvature energies

Dörfler, Willy; Nürnberg, Robert

##### Abstract:
We consider the numerical approximation of the $L$$^{2}–gradient flow of general curvature energies \int G(|\vec\varkappa|) for a curve in \mathbb{R}$$^{d}$, d ≥ 2. Here the curve can be either closed, or it can be open and clamped at the end points. These general curvature energies, and the considered boundary conditions, appear in the modelling of the power loss within an optical fibre. We present two alternative finite element approximations, both of which admit a discrete gradient flow structure. Apart from being stable, in addition, one of the methods satisfies an equidistribution property. Numerical results demonstrate the robustness and the accuracy of the proposed methods.

 Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)Sonderforschungsbereich 1173 (SFB 1173) Publikationstyp Forschungsbericht/Preprint Publikationsjahr 2018 Sprache Englisch Identifikator ISSN: 2365-662X urn:nbn:de:swb:90-878820 KITopen-ID: 1000087882 Verlag Karlsruher Institut für Technologie (KIT) Umfang 32 S. Serie CRC 1173 ; 2018/37 Schlagwörter curvature energy, gradient flow, clamped boundary conditions, finite element approximation, equidistribution, optical fibre
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