{
  "abstract": "The Scott-Vogelius element is a classical divergence-free mixed finite element for the Stokes problem that has attracted decades of research attention, yet its theoretical framework remains incomplete. In two dimensions, the inf-sup stability on Freudenthal and other regular meshes has been rigorously established. In three dimensions, Zhang established inf-sup stability on Freudenthal meshes for $k\\ge6$ in 2011, while numerical evidence indicates that inf-sup stability remains true for $k=4,5$. In this paper, we strengthen Zhang's approach and prove that the Scott--Vogelius element is inf-sup stable on Freudenthal meshes for every velocity degree $k\\ge 4$, thereby resolving a conjecture proposed by Farrell, Mitchell, and Scott in 2024. The proof proceeds by explicit constructions on local patches and does not rely on computer verification.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25690",
  "author_total": 4,
  "authors": [
    {
      "name": "Siqi Ding"
    },
    {
      "name": "Pingbing Ming"
    },
    {
      "name": "Haijun Yu"
    },
    {
      "name": "Quanfan Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/84mpbzvyeaeer.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25690",
  "fulltext_url": null,
  "id": "84mpbzvyeaeer",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25690",
  "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",
      "2206|Advanced Numerical Methods in Computational Mathematics"
    ]
  ],
  "openalex": "W7214087950",
  "pdf_url": "https://arxiv.org/pdf/2609.25690",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/84mpbzvyeaeer.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.25690",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25690"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "The Scott-Vogelius element is inf-sup stable on Freudenthal meshes for $k \\geq 4$",
  "title_text": "The Scott-Vogelius element is inf-sup stable on Freudenthal meshes for k ≥ 4",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/84mpbzvyeaeer",
  "venue": "arXiv",
  "versions": []
}