{
  "abstract": "We study the stability and consistency of Lloyd's algorithm used in combination with the Lagrangian transport of a density on a Voronoï tessellation. We show that relaxation rates as strong as $O(h^{-1/2})$, where $h$ is the mesh size, give convergence to the continuity equation in Wasserstein distance at the rate $O(h^{1/4})$. Thus the mesh can be kept regular by the correction alone, without the remeshing that Lagrangian methods usually require. An application is proposed for the compressible Euler equations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28135",
  "author_total": 2,
  "authors": [
    {
      "name": "Bruno Després"
    },
    {
      "name": "Borjan Geshkovski"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0zsdzzjzy5stz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28135",
  "fulltext_url": null,
  "id": "0zsdzzjzy5stz",
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  "landing_url": "https://inria.hal.science/hal-05762240v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
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      "hal",
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      "openalex",
      "2206|Computational Fluid Dynamics and Aerodynamics"
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  "openalex": "W7214185488",
  "pdf_url": "https://inria.hal.science/hal-05762240/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0zsdzzjzy5stz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:40Z",
      "native_id": "hal-05762240",
      "source": "hal",
      "url": "https://inria.hal.science/hal-05762240v1"
    },
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.28135",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28135"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "A Lloyd-stabilized Voronoï particle method",
  "title_text": "A Lloyd-stabilized Voronoï particle method",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/0zsdzzjzy5stz",
  "venue": "HAL",
  "versions": []
}