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Mathematics of Computation

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Error analysis for the elastic flow of parametrized curves

Authors: Klaus Deckelnick and Gerhard Dziuk
Journal: Math. Comp. 78 (2009), 645-671
MSC (2000): Primary 35K55, 65M15, 65M60
Published electronically: October 17, 2008
MathSciNet review: 2476555
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Abstract: We analyze a semidiscrete numerical scheme for approximating the evolution of parametric curves by elastic flow in $ \mathbb{R}^n$. The fourth order equation is split into two coupled second order problems, which are approximated by linear finite elements. We prove error bounds for the resulting scheme and present numerical test calculations that confirm our analysis.

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Additional Information

Klaus Deckelnick
Affiliation: Institut für Analysis und Numerik, Otto–von–Guericke–Universität Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany

Gerhard Dziuk
Affiliation: Abteilung für Angewandte Mathematik, Mathematisches Institut, Universität Frei- burg, Hermann–Herder–Str. 10, 79104 Freiburg, Germany

Received by editor(s): November 5, 2007
Received by editor(s) in revised form: April 10, 2008
Published electronically: October 17, 2008
Additional Notes: This work was supported by the Deutsche Forschungsgemeinschaft via DFG-Forschergruppe 469 Nonlinear partial differential equations: Theoretical and numerical analysis.
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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