A finite element error analysis for axisymmetric mean curvature flow. (5th August 2020)

• Record Type: Journal Article
• Authors: Barrett, John W; Deckelnick, Klaus; Nürnberg, Robert
• Is Part Of: IMA journal of numerical analysis. Volume 41:Number 3(2021)
• Page Start: 1641
• Page End: 1667
• Publication Date: 2020-08-05
• Subjects: mean curvature flow -- axisymmetry -- finite element method -- error analysis -- Angenent torus; Numerical analysis -- Periodicals; 519.405
• DOI: 10.1093/imanum/draa020
• Languages: English
• ISSNs: 0272-4979

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.