{
  "abstract": "We prove that a spatial semidiscrete finite element method preserves the stochastic maximal regularity of the heat equation on bounded convex polygonal and polyhedral domains in dimensions two and three. A main difficulty is to establish suitable Green-function estimates for stochastic convolutions, whose paths generally lack classical time derivatives. Besides, the failure of the Burkholder-Davis-Gundy (BDG) inequality at the endpoint $p=\\infty$ creates additional difficulties. Our approach leverages a hidden symmetry structure of the discrete Green's function, which enables the use of a key integration-by-parts type formula. Then the discrete stochastic maximal $L^p$-$L^p$ regularity with $p\\in [2,\\infty)$ is obtained from the discrete local energy estimates and interpolation inequalities. To extend further the discrete stochastic maximal $L^p$-$L^q$ regularity with the full range of integrability exponents, i.e., $p\\in (2,\\infty), q\\in [2,\\infty)$ or $p=q=2$, we also show that the discrete convolution kernel satisfies the stochastic Hörmander's condition, allowing the application of a stochastic version of the Calderón-Zygmund theory.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25275",
  "author_total": 3,
  "authors": [
    {
      "name": "Genming Bai"
    },
    {
      "name": "Jianbo Cui"
    },
    {
      "name": "Buyang Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f2089a3sztm05.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25275",
  "fulltext_url": null,
  "id": "f2089a3sztm05",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25275",
  "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": "W7223063029",
  "pdf_url": "https://arxiv.org/pdf/2610.25275",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f2089a3sztm05.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.25275",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25275"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Maximal $L^p$-$L^q$ regularity of finite element methods for stochastic parabolic equations in polygonal domains",
  "title_text": "Maximal L^p-L^q regularity of finite element methods for stochastic parabolic equations in polygonal domains",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/f2089a3sztm05",
  "venue": "arXiv",
  "versions": []
}