{
  "abstract": "We compute unconditional guaranteed lower eigenvalue bounds for Schrödinger operators using a modified hybrid high-order method with built-in correction for the potential defect. The method assumes exact numerical integration and allows possibly unbounded potentials in $L^p$ for $p>n/2$ and $p\\geq2$ on general polyhedral domains. We prove that the high-order correction preserves optimal a priori convergence orders, and derive reliable and efficient a posteriori error estimators. Numerical experiments provide striking evidence of optimal high-order convergence rates of the adaptive algorithm.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03567",
  "author_total": 3,
  "authors": [
    {
      "name": "Benedikt Gräßle"
    },
    {
      "name": "Moritz Hauck"
    },
    {
      "name": "Yizhou Liang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0debc90bt4akq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03567",
  "fulltext_url": null,
  "id": "0debc90bt4akq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03567",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03567",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0debc90bt4akq.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:14Z",
      "native_id": "2611.03567",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03567"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "High-order guaranteed lower bounds for the Schrödinger eigenvalue problem",
  "title_text": "High-order guaranteed lower bounds for the Schrödinger eigenvalue problem",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:28Z",
  "url": "https://research.draconitic.com/paper/0debc90bt4akq",
  "venue": "arXiv",
  "versions": []
}