{
  "abstract": "For Poisson's equation, we prove optimal algebraic convergence rates for adaptive conforming finite element methods driven by standard maximum marking in arbitrary space dimension, for every marking parameter in $(0,1]$. Previously, instance optimality of a modified maximum marking was proved in [L. Diening, C. Kreuzer, and R. Stevenson, Instance optimality of the adaptive maximum strategy, Found. Comput. Math., 16 (2016), pp. 33--68]. The basic ingredients of our anlaysis consists of discrete reliability, discrete efficiency, overlay and closure estimates of local mesh refinement. The discrete efficiency requires a facet-interior node property of simplicial mesh refinement. The novel part of the optimality analysis is an elementary integral-sum argument that converts energy decrease into a cumulative cardinality bound of marked elements, yielding rate optimality without a contraction argument.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03387",
  "author_total": 1,
  "authors": [
    {
      "name": "Yuwen Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/34830fm0amed3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03387",
  "fulltext_url": null,
  "id": "34830fm0amed3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03387",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03387",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/34830fm0amed3.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:14Z",
      "native_id": "2611.03387",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03387"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Rate optimality of AFEM with maximum marking",
  "title_text": "Rate optimality of AFEM with maximum marking",
  "type": "preprint",
  "updated_at": "2026-11-04T15:21:12Z",
  "url": "https://research.draconitic.com/paper/34830fm0amed3",
  "venue": "arXiv",
  "versions": []
}