Consistent and convergent discretizations of Helfrich-type energies on general meshes
Abstract
We show that integral curvature energies on surfaces of the type E0(M) := ∫M f(x,nM(x),D nM(x))\,dH2(x) have discrete versions for triangular complexes, where the shape operator D nM 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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