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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Error analysis for the elastic flow of parametrized curves
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by Klaus Deckelnick and Gerhard Dziuk PDF
Math. Comp. 78 (2009), 645-671 Request permission

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
  • MR Author ID: 318167
  • 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.
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 78 (2009), 645-671
  • MSC (2000): Primary 35K55, 65M15, 65M60
  • DOI: https://doi.org/10.1090/S0025-5718-08-02176-5
  • MathSciNet review: 2476555