{
  "abstract": "Building on existing $hp$-adaptive algorithms driven by equilibrated-flux estimators from [ESAIM Math. Model. Numer. Anal. 57 (2023), 329--366] and the references therein, we propose a novel $h$-adaptive algorithm for a fixed polynomial degree $p$. We consider a conforming finite element discretization of the Poisson equation in two or three space dimensions. Supposing piecewise polynomial right-hand side of degree $p-1$, we show that the algorithm yields error contraction at each step, with a contraction factor that is independent of $p$ provided that a certain {\\sl a posteriori} verifiable criterion is satisfied. We further show that this algorithm converges at optimal algebraic rate $s$ if the D\\\"orfler marking parameter is chosen below some specified $p$-independent upper threshold. The constants involved here are $p$-robust, although they may depend on the rate $s$. The theoretical results are supported by numerical experiments, in which the {\\sl a posteriori} criterion is always satisfied for one or a few local mesh refinement steps by newest-vertex bisection.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 4,
  "authors": [
    {
      "name": "Théophile Chaumont-Frelet"
    },
    {
      "name": "Zhaonan Dong"
    },
    {
      "name": "Gregor Gantner"
    },
    {
      "name": "Martin Vohralík"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f2psyy1g7vyd7.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "f2psyy1g7vyd7",
  "issns": [],
  "landing_url": "https://inria.hal.science/hal-05544956v2",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-na"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://inria.hal.science/hal-05544956/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f2psyy1g7vyd7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:33Z",
      "native_id": "hal-05544956",
      "source": "hal",
      "url": "https://inria.hal.science/hal-05544956v2"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-na",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "On $p$-robust convergence and optimality of adaptive FEM driven by equilibrated-flux estimators",
  "title_text": "On p-robust convergence and optimality of adaptive FEM driven by equilibrated-flux estimators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:33Z",
  "url": "https://research.draconitic.com/paper/f2psyy1g7vyd7",
  "venue": "HAL",
  "versions": []
}