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Discrete anisotropic curvature flow of graphs

Published online by Cambridge University Press:  15 August 2002

Klaus Deckelnick  and
Gerhard Dziuk
Klaus Deckelnick
Affiliation:
Institut für Angewandte Mathematik, Hermann–Herder–Straße 10, 79104 Freiburg i. Br., Germany. gerd@mathematik.uni-freiburg.de.
Gerhard Dziuk
Affiliation:
Institut für Angewandte Mathematik, Hermann–Herder–Straße 10, 79104 Freiburg i. Br., Germany. gerd@mathematik.uni-freiburg.de.
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Abstract

The evolution of n–dimensional graphs under a weighted curvature flow is approximated by linear finite elements. We obtain optimal error bounds for the normals and the normal velocities of the surfacesin natural norms. Furthermore we prove a global existence result for thecontinuous problem and present some examples of computed surfaces.

Keywords

Mean curvature flowanisotropicfinite elementsconvergence.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 33 , Issue 6 , November 1999 , pp. 1203 - 1222
Copyright
© EDP Sciences, SMAI, 1999

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