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arXiv · 2302.01705

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

Vincent Degrooff·Peter Gladbach·Heiner Olbermann
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Abstract

We show that integral curvature energies on surfaces of the type $E_0(M) := \int_M f(x,n_M(x),D n_M(x))\,d\mathcal{H}^2(x)$ have discrete versions for triangular complexes, where the shape operator $D n_M$ 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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Vincent Degrooff, Peter Gladbach, Heiner Olbermann. 2023-02-03. Consistent and convergent discretizations of Helfrich-type energies on general meshes. https://arxiv.org/abs/2302.01705

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