We introduce a novel formulation for the evolution of parametric curves by anisotropic curve shortening flow in Rd , d ≥ 2. 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.
Discrete anisotropic curve shortening flow in higher codimension / Deckelnick, Klaus; Nürnberg, Robert. - In: IMA JOURNAL OF NUMERICAL ANALYSIS. - ISSN 0272-4979. - 45:(2025), pp. 36-67. [10.1093/imanum/drae015]
Discrete anisotropic curve shortening flow in higher codimension
Nürnberg, Robert
2025-01-01
Abstract
We introduce a novel formulation for the evolution of parametric curves by anisotropic curve shortening flow in Rd , d ≥ 2. 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.File | Dimensione | Formato | |
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