{
  "abstract": "The stochastic Landau--Lifshitz--Gilbert (sLLG) equation is a strongly nonlinear stochastic PDE with a non-convex pointwise constraint arising in the theory of micromagnetics. We analyse a fully discrete, structure-preserving finite element approximation of the sLLG equation with coloured multiplicative Stratonovich noise on a bounded interval. The method utilises continuous piecewise affine finite elements, mass lumping, and midpoint time discretisation to preserve the unit-length constraint exactly at the finite element nodes. Under suitable regularity assumptions on the initial data and the noise, we establish uniform higher-moment stability and develop an error analysis for the scheme. The analysis exploits the geometric structure of the equation and the stochastic midpoint discretisation. For every $γ\\in(0,\\frac12)$, we prove first-order spatial convergence and temporal convergence of order $γ$ in the natural discrete energy norm, locally in mean square on events of arbitrarily large probability and, consequently, in probability. To the best of our knowledge, this is the first convergence-rate result for a fully discrete structure-preserving finite element scheme solving the stochastic Landau--Lifshitz--Gilbert equation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06459",
  "author_total": 1,
  "authors": [
    {
      "name": "Agus L. Soenjaya"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0g5td4r8gwwhk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06459",
  "fulltext_url": null,
  "id": "0g5td4r8gwwhk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06459",
  "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.AP"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2612|Numerical methods for differential equations"
    ]
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  "openalex": "W7212031406",
  "pdf_url": "https://arxiv.org/pdf/2609.06459",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0g5td4r8gwwhk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.06459",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06459"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Rate of convergence of a fully discrete structure-preserving midpoint scheme for the stochastic Landau--Lifshitz--Gilbert equation",
  "title_text": "Rate of convergence of a fully discrete structure-preserving midpoint scheme for the stochastic Landau--Lifshitz--Gilbert equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/0g5td4r8gwwhk",
  "venue": "arXiv",
  "versions": []
}