{
  "abstract": "We give a one-sided stability argument for high-order cut finite elements with symmetric Nitsche boundary conditions. On each boundary patch, an $H^1$-projection splits the discrete function into a single polynomial and a stabilized residual. Inward segments control the polynomial inside the physical domain; complete-element estimates control only the residual. For smooth exterior boundaries and under a geometry-dependent mesh restriction, this gives an explicit normal-flux estimate with factor $p^2/h$ and a sufficient Nitsche penalty with the same scaling. The constants are independent of the cut position and polynomial degree. A neighboring-interval estimate quantifies the exponential cost of polynomial continuation and motivates avoiding it in the stability proof. We obtain $hp$-error estimates, with half a power of degree lost in energy and a full power in $L^2$ relative to best approximation, and exponential degree convergence for analytic extensions on sufficiently fine meshes. Translated-disk experiments show bounded normalized flux constants and penalty thresholds over the tested degrees and cuts, and resolved convergence curves follow the predicted orders. Physical and extension-dependent stabilization errors are reported separately.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34853",
  "author_total": 4,
  "authors": [
    {
      "name": "Erik Burman"
    },
    {
      "name": "Peter Hansbo"
    },
    {
      "name": "Mats G. Larson"
    },
    {
      "name": "Karl Larsson"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/47aq4hmrze1ph.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34853",
  "fulltext_url": null,
  "id": "47aq4hmrze1ph",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34853",
  "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": "W7223846826",
  "pdf_url": "https://arxiv.org/pdf/2610.34853",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/47aq4hmrze1ph.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.34853",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34853"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "One-Sided $p$-Explicit Stability for High-Order Cut Finite Element Nitsche Methods",
  "title_text": "One-Sided p-Explicit Stability for High-Order Cut Finite Element Nitsche Methods",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/47aq4hmrze1ph",
  "venue": "arXiv",
  "versions": []
}