Convergence of a finite element method for non-parametric mean curvature flow

1995 ◽  
Vol 72 (2) ◽  
pp. 197-222 ◽  
Author(s):  
Klaus Deckelnick ◽  
Gerhard Dziuk
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Element Method ◽  
Non Parametric

scholarly journals A convergent evolving finite element algorithm for mean curvature flow of closed surfaces

2019 ◽  
Vol 143 (4) ◽  
pp. 797-853 ◽  
Author(s):  
Balázs Kovács ◽  
Buyang Li ◽  
Christian Lubich
Keyword(s):  
Finite Element ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Closed Surfaces ◽  
Element Algorithm

scholarly journals A finite element error analysis for axisymmetric mean curvature flow

2020 ◽  
Author(s):  
John W Barrett ◽  
Klaus Deckelnick ◽  
Robert Nürnberg
Keyword(s):  
Finite Element ◽  
Mean Curvature ◽  
Numerical Approximation ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Optimal Error ◽  
Fully Discrete ◽  
Fully Discrete Approximation ◽  
Element Error ◽  
Theoretical Results

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.

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