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

02/03/2023

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by   Peter Gladbach, et al.

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We show that integral curvature energies on surfaces of the type E_0(M) := ∫_M f(x,n_M(x),D n_M(x)) dℋ^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.