{
  "abstract": "We analyse symmetric interior-penalty discontinuous Galerkin approximations of elliptic stochastic partial differential equations driven by spatial Gaussian white noise on quasi-uniform polytopic meshes. The low regularity of the exact random field precludes the usual SIP consistency argument. We instead restrict the same continuum white-noise functional canonically to the discontinuous polynomial space and separate the error into stochastic forcing-restriction and deterministic discretisation components. For every fixed polynomial degree $k\\geq1$, we prove the sharp two-sided estimate \\[ \\|Y-Y_h\\|_{L^2(Ξ;L^2(Ω))} \\simeq h^{2-d/2}, \\] giving rates $h$ in two dimensions and $h^{1/2}$ in three dimensions. A finite-dimensional lower bound establishes optimality. The analysis allows polytopic elements with arbitrarily many and arbitrarily small faces, including admissible non-convex elements. In two dimensions we also treat polygons with a single reentrant corner. Although the deterministic approximation exhibits an angle-dependent loss of regularity, the singular resolvent contribution is finite rank, and the sharp first-order stochastic rate is retained. The discontinuous structure yields an exact element-local sampler for the restricted white noise. Numerical experiments on irregular polygonal, non-convex polytopic and reentrant domains support the predicted convergence behaviour.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06082",
  "author_total": 1,
  "authors": [
    {
      "name": "Tristan Pryer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bzb34ftqa1hf1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06082",
  "fulltext_url": null,
  "id": "bzb34ftqa1hf1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06082",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2206|Advanced Numerical Methods in Computational Mathematics"
    ]
  ],
  "openalex": "W7212079680",
  "pdf_url": "https://arxiv.org/pdf/2609.06082",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bzb34ftqa1hf1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.06082",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06082"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Polytopic symmetric interior-penalty approximation of elliptic SPDEs driven by spatial white noise",
  "title_text": "Polytopic symmetric interior-penalty approximation of elliptic SPDEs driven by spatial white noise",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/bzb34ftqa1hf1",
  "venue": "arXiv",
  "versions": []
}