{
  "abstract": "We present a unifying framework to construct local Fortin operators for conforming mixed finite element pairs for the Stokes equations. The operators are constructed to satisfy the divergence-preservation property, local stability and approximation properties, and certain trace-preservation properties. For the latter, some of the finite element pairs require an enrichment of the velocity space. We present the construction for the $P_d-P_0$ element, the Bernardi-Raugel element, the conforming Crouzeix-Raviart element, a modified MINI element and generalised Taylor-Hood elements. Furthermore, we discuss implications of the existence of such a Fortin operator beyond inf-sup stability. These include applications to non-Newtonian fluid flow, problems with inhomogeneous Dirichlet boundary conditions, as well as uniform inf-sup stability relevant for domain approximation and moving domains.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04926",
  "author_total": 2,
  "authors": [
    {
      "name": "Franziska Eickmann"
    },
    {
      "name": "Tabea Tscherpel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/apmydc0hkby5a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04926",
  "fulltext_url": null,
  "id": "apmydc0hkby5a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.04926",
  "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": "W7211878890",
  "pdf_url": "https://arxiv.org/pdf/2609.04926",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/apmydc0hkby5a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.04926",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04926"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Construction of trace-preserving Fortin operators",
  "title_text": "Construction of trace-preserving Fortin operators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/apmydc0hkby5a",
  "venue": "arXiv",
  "versions": []
}