An unconditionally stable finite element scheme for anisotropic curve shortening flow

Klaus Deckelnick; Robert Nürnberg

Archivum Mathematicum (2023)

  • Volume: 059, Issue: 3, page 263-274
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Deckelnick, Klaus, and Nürnberg, Robert. "An unconditionally stable finite element scheme for anisotropic curve shortening flow." Archivum Mathematicum 059.3 (2023): 263-274. <http://eudml.org/doc/298988>.

@article{Deckelnick2023,
abstract = {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.},
author = {Deckelnick, Klaus, Nürnberg, Robert},
journal = {Archivum Mathematicum},
keywords = {anisotropic curve shortening flow; finite element method; stability},
language = {eng},
number = {3},
pages = {263-274},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {An unconditionally stable finite element scheme for anisotropic curve shortening flow},
url = {http://eudml.org/doc/298988},
volume = {059},
year = {2023},
}

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
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 059
IS - 3
SP - 263
EP - 274
AB - 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.
LA - eng
KW - anisotropic curve shortening flow; finite element method; stability
UR - http://eudml.org/doc/298988
ER -

References

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