{
  "abstract": "Anisotropic error estimates are determined for the $L^2$-orthogonal projection onto discontinuous finite element spaces in two and three dimensions. These estimates are determined in $W^{m,p}$-seminorms, in which $p \\in [1,\\infty]$ and $0 \\le m \\le k+1$, where $k \\ge 0$ is the polynomial degree. The analysis relies on a geometric condition that is equivalent to the maximum angle condition. As an application, an apriori error analysis is presented for a hybridizable discontinuous Galerkin discretization of the Poisson problem on two and three dimensional anisotropic meshes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38892",
  "author_total": 3,
  "authors": [
    {
      "name": "Joaquín Valenzuela Díaz"
    },
    {
      "name": "Yuan Wang"
    },
    {
      "name": "Sander Rhebergen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1yet63jqfdna4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38892",
  "fulltext_url": null,
  "id": "1yet63jqfdna4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38892",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
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      "arxiv",
      "math.NA"
    ]
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  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38892",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1yet63jqfdna4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38892",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38892"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Anisotropic error estimates for the $L^{2}$-projection onto discontinuous finite element spaces",
  "title_text": "Anisotropic error estimates for the L^2-projection onto discontinuous finite element spaces",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/1yet63jqfdna4",
  "venue": "arXiv",
  "versions": []
}