A finite element error analysis for axisymmetric mean curvature flow
File(s)1911.05398v1.pdf (875.83 KB)
Working paper
Author(s)
Barrett, John W
Deckelnick, Klaus
Nürnberg, Robert
Type
Working Paper
Abstract
We consider the numerical approximation of axisymmetric mean curvature flow
with the help of linear finite elements. In the case of a closed genus-1
surface, we derive optimal error bounds with respect to the $L^2$-- and
$H^1$--norms for a fully discrete approximation. We perform convergence
experiments to confirm the theoretical results, and also present numerical
simulations for some genus-0 and genus-1 surfaces.
with the help of linear finite elements. In the case of a closed genus-1
surface, we derive optimal error bounds with respect to the $L^2$-- and
$H^1$--norms for a fully discrete approximation. We perform convergence
experiments to confirm the theoretical results, and also present numerical
simulations for some genus-0 and genus-1 surfaces.
Date Issued
2019-11-13
Citation
2019
Publisher
arXiv
Copyright Statement
© 2019 The Author(s)
Identifier
http://arxiv.org/abs/1911.05398v1
Subjects
math.NA
math.NA
cs.NA
65M60, 65M12, 65M15, 53C44, 35K55
Notes
20 pages, 7 figures
Publication Status
Published