{
  "abstract": "In this paper, we consider the Smagorinsky model for the Navier-Stokes equations within a virtual element framework. Under the standard assumption of small data, we prove the existence and uniqueness of a solution. Assuming more regularity to the solutions, we derive the known convergence rates $h$ for the a priori error estimates of the Smagorinsky model in two dimensional domains. We additionally prove that divergence-free virtual discretizations provide improved convergence orders, with weaker regularity assumptions than in the finite element literature. We conclude the paper with numerical results that corroborate the theory.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02433",
  "author_total": 3,
  "authors": [
    {
      "name": "Karol L. Cascavita"
    },
    {
      "name": "Francesca Marcon"
    },
    {
      "name": "Maria Strazzullo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1nxj3evw23qc0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02433",
  "fulltext_url": null,
  "id": "1nxj3evw23qc0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02433",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2206|Advanced Numerical Methods in Computational Mathematics"
    ]
  ],
  "openalex": "W7207830888",
  "pdf_url": "https://arxiv.org/pdf/2609.02433",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1nxj3evw23qc0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.02433",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02433"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Numerical Analysis of the Virtual Element Approximation for the Smagorinsky Turbulence Model",
  "title_text": "Numerical Analysis of the Virtual Element Approximation for the Smagorinsky Turbulence Model",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/1nxj3evw23qc0",
  "venue": "arXiv",
  "versions": []
}