{
  "abstract": "We establish nearly sharp $W^{1,\\infty}$ stability estimates for the Legendre spectral Ritz projection associated with Laplacian on a square domain. Its norm grows proportionally to the square root of the polynomial degree, up to a cubic logarithmic factor. The upper bound uses an integral representation of the discrete gradient projection in terms of one-dimensional semigroup kernels and a rank-two Duhamel comparison between the mass-matrix semigroup and its infinite-dimensional counterpart. The lower bound follows from the endpoint concentration of the Legendre kernel. As an application, we derive gradient maximum-norm error estimates for the Poisson and heat equations, with spatial factors optimal up to logarithmic terms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19531",
  "author_total": 2,
  "authors": [
    {
      "name": "Yongxing Guo"
    },
    {
      "name": "Yuwen Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8vsshqps302rc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19531",
  "fulltext_url": null,
  "id": "8vsshqps302rc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19531",
  "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": "W7222189287",
  "pdf_url": "https://arxiv.org/pdf/2610.19531",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8vsshqps302rc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19531",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19531"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Nearly sharp $W^{1,\\infty}$ stability of polynomial spectral Ritz projections",
  "title_text": "Nearly sharp W^1,∞ stability of polynomial spectral Ritz projections",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/8vsshqps302rc",
  "venue": "arXiv",
  "versions": []
}