{
  "abstract": "On triangular meshes, we analyze local mesh refinement based on longest-edge bisection equipped with the serial longest-edge propagation-path closure. Ties are resolved by terminal priority: if the incoming shared edge is a longest edge of the neighboring triangle, the pair is declared terminal and that edge is bisected. For every adaptive mesh sequence $\\mathcal{T}_0, \\mathcal{T}_1, \\ldots, \\mathcal{T}_L$ with a sequence of marked sets $\\mathcal{M}_0, \\mathcal{M}_1, \\ldots, \\mathcal{M}_{L-1}$, we prove the cumulative closure estimate $$\\#\\mathcal{T}_L-\\#\\mathcal{T}_0 \\lesssim\\sum_{\\ell=0}^{L-1}\\#\\mathcal{M}_\\ell.$$ The proof derives single-mark locality from the uniform multiplicative gap between possible descendant diameters implied by finite similarity classes, and converts this locality into the cumulative estimate through a Binev--Dahmen--DeVore-type charging argument.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04003",
  "author_total": 2,
  "authors": [
    {
      "name": "Yuwen Li"
    },
    {
      "name": "Zhiyuan Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/80pmzyn7e394w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04003",
  "fulltext_url": null,
  "id": "80pmzyn7e394w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.04003",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "1704|Computational Geometry and Mesh Generation"
    ]
  ],
  "openalex": "W7208722826",
  "pdf_url": "https://arxiv.org/pdf/2609.04003",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/80pmzyn7e394w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.04003",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04003"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Closure complexity of longest-edge bisection for triangular meshes",
  "title_text": "Closure complexity of longest-edge bisection for triangular meshes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/80pmzyn7e394w",
  "venue": "arXiv",
  "versions": []
}