Discrete anisotropic curve shortening flow in higher codimension
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909472180404224 |
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| author | Deckelnick, Klaus Nürnberg, Robert |
| author_facet | Deckelnick, Klaus Nürnberg, Robert |
| contents | We introduce a novel formulation for the evolution of parametric curves by anisotropic curve shortening flow in ${\mathbb R}^d$, $d\geq2$. The reformulation hinges on a suitable manipulation of the parameterization's tangential velocity, leading to a strictly parabolic differential equation. Moreover, the derived equation is in divergence form, giving rise to a natural variational numerical method. For a fully discrete finite element approximation based on piecewise linear elements we prove optimal error estimates. Numerical simulations confirm the theoretical results and demonstrate the practicality of the method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_02138 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Discrete anisotropic curve shortening flow in higher codimension Deckelnick, Klaus Nürnberg, Robert Numerical Analysis We introduce a novel formulation for the evolution of parametric curves by anisotropic curve shortening flow in ${\mathbb R}^d$, $d\geq2$. The reformulation hinges on a suitable manipulation of the parameterization's tangential velocity, leading to a strictly parabolic differential equation. Moreover, the derived equation is in divergence form, giving rise to a natural variational numerical method. For a fully discrete finite element approximation based on piecewise linear elements we prove optimal error estimates. Numerical simulations confirm the theoretical results and demonstrate the practicality of the method. |
| title | Discrete anisotropic curve shortening flow in higher codimension |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2310.02138 |