| Issue |
ESAIM: M2AN
Volume 33, Number 6, November December 1999
|
|
|---|---|---|
| Page(s) | 1203 - 1222 | |
| DOI | https://doi.org/10.1051/m2an:1999141 | |
| Published online | 15 August 2002 | |
Discrete anisotropic curvature flow of graphs
Institut für Angewandte Mathematik, Hermann–Herder–Straße 10,
79104 Freiburg i. Br., Germany. gerd@mathematik.uni-freiburg.de.
Received:
9
January
1997
Revised:
21
November
1997
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 surfaces in natural norms. Furthermore we prove a global existence result for the continuous problem and present some examples of computed surfaces.
Résumé
L'évolution de graphes n-dimensionnels selon le problème de flot à courbure pondérée est approchée par des éléments finis linéaires. On obtient des bornes d'erreurs optimales pour les normales et pour les vitesses normales des surfaces, dans des normes naturelles. De plus, nous établissons un théorème d'existence globale pour le problème continu et nous présentons quelques exemples numériques d'évolution de surfaces.
Mathematics Subject Classification: 65N30 / 35K65
Key words: Mean curvature flow / anisotropic / finite elements / convergence.
© EDP Sciences, SMAI, 1999
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