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Adaptive moving mesh methods for isotropic/anisotropic mean curvature flow with axisymmetric geometry — arXiv:2609.13883

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.13883
License (as archived): CC0-1.0
Archived: 2026-10-16T01:22:28.014Z
SHA-256 of the archived text: cb2c95f946e43808d669f094b27d89710e0b062b12d71c7ea44abcb7b0074a4f
Stable URL of this page: https://metraipolis.com/documento/dc_97aba663ecf4

How to cite

Adaptive moving mesh methods for isotropic/anisotropic mean curvature flow with axisymmetric geometry — arXiv:2609.13883 — arXiv (en), https://arxiv.org/abs/2609.13883 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_97aba663ecf4 (Metraipolis archive dc_97aba663ecf4, sha256 cb2c95f946e43808d669f094b27d89710e0b062b12d71c7ea44abcb7b0074a4f)

BibTeX

@misc{dc97aba663ecf4,
  title = {Adaptive moving mesh methods for isotropic/anisotropic mean curvature flow with axisymmetric geometry — arXiv:2609.13883},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.13883},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_97aba663ecf4; sha256 cb2c95f946e43808d669f094b27d89710e0b062b12d71c7ea44abcb7b0074a4f},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.13883. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

This paper introduces adaptive moving mesh methods for the numerical simulation of axisymmetric mean curvature flow, addressing both isotropic and anisotropic cases. The methods are developed within the framework of the mesh equidistribution principle, where a carefully designed tangential velocity is employed to dynamically redistribute mesh points during the evolution. To accurately capture the key geometric features of the evolving interfaces, we select monitor functions based on the curvature $\kappa$, its arc-length derivative $\kappa_s$, and the squared curvature $\kappa^2$. These monitor functions can be flexibly tailored to suit different problem settings and play a vital role in determining the resulting mesh quality and numerical accuracy. Spatial discretization is performed using central finite differences, while temporal integration is handled with first- and second-order time-stepping schemes, including the BDFk ($k=1,2$) and Crank-Nicolson methods. Additionally, a Lagrange multiplier approach is incorporated into the adaptive system to enforce the underlying geometric constraint, resulting in energy-stable numerical schemes. Numerical experiments confirm the convergence and energy stability of the proposed methods. More importantly, the results clearly show that the proposed methods offer significant advantages in complex geometric evolutions: by utilizing appropriately designed monitor functions, the adaptive methods achieve dynamic redistribution of mesh points, efficiently capturing localized geometric features, significantly improving numerical accuracy, and effectively preventing mesh degeneration, particularly in anisotropic cases.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-15 in math.NA).
Categorie arXiv: Numerical Analysis (math.NA).
Pagina del lavoro: https://arxiv.org/abs/2609.13883 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-16T00:39:06.294Z dalla pagina https://arxiv.org/catchup/math.NA/2026-09-15?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).