A finite element error analysis for axisymmetric mean curvature flow-Reference-Cited by-同舟云学术

A finite element error analysis for axisymmetric mean curvature flow

Published:2020-08-05 Issue:3 Volume:41 Page:1641-1667
ISSN:0272-4979
Container-title:IMA Journal of Numerical Analysis
language:en
Short-container-title:

Author:

Barrett John W¹,Deckelnick Klaus²,Nürnberg Robert¹

Affiliation:

1. Department of Mathematics, Imperial College London, London, SW7 2AZ, UK

2. Institut für Analysis und Numerik, Otto-von-Guericke-Universität Magdeburg, 39106 Magdeburg, Germany

Abstract

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, including for the Angenent torus.

Publisher

Oxford University Press (OUP)

Subject

Applied Mathematics,Computational Mathematics,General Mathematics

Link

http://academic.oup.com/imajna/article-pdf/41/3/1641/38983508/draa020.pdf

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