{
  "abstract": "We analyse a divergence form stochastic differential equation featuring a Leray-Lions flux function that satisfies standard Carathéodory, growth, monotonicity, and coercivity conditions. We consider two types of noise: multiplicative Lipschitz continuous noise and a transport noise. Our approach utilises the gradient discretisation method, a generic framework encompassing various numerical schemes such as conforming and nonconforming finite element methods, hybrid mimetic mixed methods, and hybrid high order methods. For both types of noise, we propose a stable generic scheme, prove that scheme solutions converge to a strong solution in the probabilistic sense. For the multiplicative Lipschitz continuous noise, we establish the rate of convergence.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05171",
  "author_total": 2,
  "authors": [
    {
      "name": "Ngan Le"
    },
    {
      "name": "Huateng Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f4v9vb5yhp96z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05171",
  "fulltext_url": null,
  "id": "f4v9vb5yhp96z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05171",
  "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"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2206|Advanced Numerical Methods in Computational Mathematics"
    ]
  ],
  "openalex": "W7220732008",
  "pdf_url": "https://arxiv.org/pdf/2610.05171",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f4v9vb5yhp96z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05171",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05171"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Convergence and error analysis for numerical approximations of stochastic Leray-Lions equations",
  "title_text": "Convergence and error analysis for numerical approximations of stochastic Leray-Lions equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/f4v9vb5yhp96z",
  "venue": "arXiv",
  "versions": []
}