Geodesic
An unconditionally stable finite element scheme for anisotropic curve shortening flow
Archivum mathematicum, Tome 59 (2023) no. 3, pp. 263-274.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

Based on a recent novel formulation of parametric anisotropic curve shortening flow, we analyse a fully discrete numerical method of this geometric evolution equation. The method uses piecewise linear finite elements in space and a backward Euler approximation in time. We establish existence and uniqueness of a discrete solution, as well as an unconditional stability property. Some numerical computations confirm the theoretical results and demonstrate the practicality of our method.
DOI : 10.5817/AM2023-3-263
Classification : 35K15, 53E10, 65M12, 65M60
Keywords: anisotropic curve shortening flow; finite element method; stability 
@article{10_5817_AM2023_3_263,
     author = {Deckelnick, Klaus and N\"urnberg, Robert},
     title = {An unconditionally stable finite element scheme for anisotropic curve shortening flow},
     journal = {Archivum mathematicum},
     pages = {263--274},
     publisher = {mathdoc},
     volume = {59},
     number = {3},
     year = {2023},
     doi = {10.5817/AM2023-3-263},
     mrnumber = {4563038},
     zbl = {07675596},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5817/AM2023-3-263/}
}
TY  - JOUR
AU  - Deckelnick, Klaus
AU  - Nürnberg, Robert
TI  - An unconditionally stable finite element scheme for anisotropic curve shortening flow
JO  - Archivum mathematicum
PY  - 2023
SP  - 263
EP  - 274
VL  - 59
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.5817/AM2023-3-263/
DO  - 10.5817/AM2023-3-263
LA  - en
ID  - 10_5817_AM2023_3_263
ER  - 
%0 Journal Article
%A Deckelnick, Klaus
%A Nürnberg, Robert
%T An unconditionally stable finite element scheme for anisotropic curve shortening flow
%J Archivum mathematicum
%D 2023
%P 263-274
%V 59
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.5817/AM2023-3-263/
%R 10.5817/AM2023-3-263
%G en
%F 10_5817_AM2023_3_263
Deckelnick, Klaus; Nürnberg, Robert. An unconditionally stable finite element scheme for anisotropic curve shortening flow. Archivum mathematicum, Tome 59 (2023) no. 3, pp. 263-274. doi : 10.5817/AM2023-3-263. http://geodesic.mathdoc.fr/articles/10.5817/AM2023-3-263/

Cité par Sources :