A finite element error analysis for axisymmetric mean curvature flow

11/13/2019

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by   John W. Barrett, et al.

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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.