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Error analysis for the elastic flow of parametrized curves
Author(s):
Klaus
Deckelnick;
Gerhard
Dziuk.
Journal:
Math. Comp.
78
(2009),
645-671.
MSC (2000):
Primary 35K55, 65M15, 65M60
Posted:
October 17, 2008
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Abstract:
We analyze a semidiscrete numerical scheme for approximating the evolution of parametric curves by elastic flow in  . 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.
References:
-
- 1.
- J.W. Barrett, H. Garcke, R. Nürnberg, A parametric finite element method for fourth order geometric evolution equations, J. Comput. Phys. 222(1) (2007), 441-467. MR 2298053 (2008a:65176)
- 2.
- K. Deckelnick, G. Dziuk, Error analysis of a finite element method for the Willmore flow of graphs, Interfaces Free Bound. 8 (2006), 21-46. MR 2231251 (2007d:65083)
- 3.
- K. Deckelnick, G. Dziuk, C.M. Elliott, Computation of geometric partial differential equations and mean curvature flow, Acta Numer. 14 (2005), 139-232. MR 2168343 (2006h:65159)
- 4.
- G. Dziuk, Computational parametric Willmore flow, Preprint Fakultät für Mathematik und Physik 07-13 (2007).
- 5.
- G. Dziuk, E. Kuwert, R. Schätzle, Evolution of elastic curves in
 : Existence and computation, SIAM J. Math. Anal. 33 (2002), 1228-1245. MR 1897710 (2003f:53117) - 6.
- A. Polden, Curves and surfaces of least total curvature and fourth-order flows, Ph.D. dissertation, Universität Tübingen, Tübingen, Germany, 1996.
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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
DOI:
10.1090/S0025-5718-08-02176-5
PII:
S 0025-5718(08)02176-5
Received by editor(s):
November 5, 2007
Received by editor(s) in revised form:
April 10, 2008
Posted:
October 17, 2008
Additional Notes:
This work was supported by the Deutsche Forschungsgemeinschaft via DFG-Forschergruppe 469 {\it Nonlinear partial differential equations: Theoretical and numerical analysis}.
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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