{
  "abstract": "This paper investigates finite element approximations of the one-dimensional viscous stochastic Burgers equation with additive trace-class noise. For the $P_2$ finite element spatial semi-discretization, we derive strong error estimates that are optimal with respect to regularity in \\(L^p([0,T] \\times Ω;H_{D}^{α,q})\\) for \\(p,q\\in[2,\\infty)\\) and \\(α\\in[-1,0]\\), as well as an almost regularity-optimal estimate in \\(L^p(Ω;C([0,T];L^\\infty(\\mathcal{O})))\\). Furthermore, we derive weak error estimates for moments of both terminal $L^q$-norms and space-time $L^p(0,T;L^q(\\mathcal{O}))$-norms, with weak convergence rates (nearly) twice the corresponding strong ones. For the fully discrete scheme, which combines the \\(P_2\\) finite element method in space with a drift-implicit Euler--Maruyama scheme in time, we establish a strong temporal convergence rate of order \\(τ^{1/2-\\varepsilon}\\) in a discrete analogue of \\(L^p(Ω;C([0,T];L^\\infty(\\mathcal{O})))\\), under the condition \\(τ\\leqslant h^2\\). Numerical experiments are presented to illustrate the theoretical convergence rates.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11584",
  "author_total": 3,
  "authors": [
    {
      "name": "Binjie Li"
    },
    {
      "name": "Xiaoping Xie"
    },
    {
      "name": "Qin Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f6zz14k4n1z6s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11584",
  "fulltext_url": null,
  "id": "f6zz14k4n1z6s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11584",
  "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": "W7212288167",
  "pdf_url": "https://arxiv.org/pdf/2609.11584",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f6zz14k4n1z6s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.11584",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11584"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Convergence of finite element approximations for the one-dimensional stochastic Burgers equation with additive trace-class noise",
  "title_text": "Convergence of finite element approximations for the one-dimensional stochastic Burgers equation with additive trace-class noise",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/f6zz14k4n1z6s",
  "venue": "arXiv",
  "versions": []
}