Consistent and convergent discretizations of Helfrich-type energies on general meshes
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...
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| Main Authors: | , |
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| Format: | Journal Article |
| Language: | English |
| Published: |
03-02-2023
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| Subjects: | |
| Online Access: | Get full text |
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| Summary: | 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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| DOI: | 10.48550/arxiv.2302.01705 |