Consistent and convergent discretizations of Helfrich-type energies on general meshes

Gladbach, Peter;Olbermann, Heiner
(2023) arxiv.org — (2023)

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We show that certain integral curvature energies on surfaces have discrete versions for triangular complexes, where the shape operator is replaced by the piecewise gradient of a piecewise affine edge director field. We combine an ansatz-free asymptotic lower bound for any uniform approximation of a surface with triangular complexes and a recovery sequence consisting of any regular triangulation of the limit sequence and an almost optimal choice of edge director.
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Gladbach, P., & Olbermann, H. (2023). Consistent and convergent discretizations of Helfrich-type energies on general meshes. arxiv.org. Submitted. https://hdl.handle.net/2078.5/236500 (Original work published 2023)