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UnCut FEM with PHT-splines on unfitted T-meshes — arXiv:2610.09909

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.09909
License (as archived): CC0-1.0
Archived: 2026-10-08T12:43:43.042Z
SHA-256 of the archived text: b07cbac8ee45d01d074fcacb998305643cc1f70b8a11dbfb9978c9b421b56b7b
Stable URL of this page: https://metraipolis.com/documento/dc_bf804da4e53d

How to cite

UnCut FEM with PHT-splines on unfitted T-meshes — arXiv:2610.09909 — arXiv (en), https://arxiv.org/abs/2610.09909 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_bf804da4e53d (Metraipolis archive dc_bf804da4e53d, sha256 b07cbac8ee45d01d074fcacb998305643cc1f70b8a11dbfb9978c9b421b56b7b)

BibTeX

@misc{dcbf804da4e53d,
  title = {UnCut FEM with PHT-splines on unfitted T-meshes — arXiv:2610.09909},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.09909},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_bf804da4e53d; sha256 b07cbac8ee45d01d074fcacb998305643cc1f70b8a11dbfb9978c9b421b56b7b},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.09909. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We propose a novel unfitted finite element method based on polynomial splines over hierarchical T-meshes (PHT-splines) for elliptic partial differential equations (PDEs) posed on domains whose boundaries are described implicitly by a level-set function. Exploiting the enhanced smoothness of the spline space, we formulate the method by minimizing the $L^2$ residual of the PDE over an extended neighborhood of the physical domain. This formulation allows the method to be implemented entirely on the background mesh using standard element-wise quadrature. It yields a symmetric positive-definite linear system and avoids the geometric construction of curved cut subregions in boundary elements, as well as the associated nontrivial numerical integration. We establish well-posedness of the numerical scheme and derive optimal \emph{a priori} error estimates in the $H^1$ norm. In addition, we employ a residual-based \emph{a posteriori} error indicator to guide local adaptive refinement of the hierarchical T-meshes. Numerical experiments corroborate the theoretical results and demonstrate the accuracy and efficiency of the proposed approach.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.NA, nuovi lavori del giorno).
Categorie arXiv: Numerical Analysis (math.NA).
Pagina del lavoro: https://arxiv.org/abs/2610.09909 — 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 2026-10-08T12:16:45.221Z dalla pagina https://arxiv.org/list/math.NA/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).