# Stable approximations for axisymmetric Willmore flow for closed and open surfaces

@article{Barrett2019StableAF, title={Stable approximations for axisymmetric Willmore flow for closed and open surfaces}, author={John W. Barrett and Harald Garcke and Robert N{\"u}rnberg}, journal={ArXiv}, year={2019}, volume={abs/1911.01132} }

For a hypersurface in ℝ3, Willmore flow is defined as the L2-gradient flow of the classical Willmore energy: the integral of the squared mean curvature. This geometric evolution law is of interest in differential geometry, image reconstruction and mathematical biology. In this paper, we propose novel numerical approximations for the Willmore flow of axisymmetric hypersurfaces. For the semidiscrete continuous-in-time variants we prove a stability result. We consider both closed surfaces, and…

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