{
  "abstract": "In this work, we develop and analyze a splitting mixed finite element method, combined with a fully implicit Euler time discretization, for a stochastic Keller--Segel system with general polynomial logistic growth and multiplicative noise. The proposed splitting formulation allows the use of standard finite element spaces without requiring the LBB inf--sup condition associated with traditional mixed finite element methods and, at each time step, avoids the need for solving a coupled nonlinear system. We first establish the well-posedness of the variational solution and derive new high-moment, higher-order regularity, and exponential stability estimates. These estimates provide the key analytical foundation for the strong convergence analysis of the numerical method. A principal contribution of this work is the derivation of error estimates directly in full expectation, without the use of localization arguments. By combining the new stability and regularity estimates with a stochastic Gronwall framework, we overcome the difficulties arising from the interaction between the nonlinear chemotactic coupling and the multiplicative noise. As a result, we establish strong convergence in high-moment norms and obtain optimal convergence rates with respect to both the temporal and spatial discretizations. In particular, the proposed method achieves the optimal rates of order $k^{\\frac{1}{2}}$ in time and $h$ in space in the relevant $L^2$- and $H^1$-based error norms. These results provide, to our knowledge, the first optimal strong convergence analysis in full expectation for a splitting mixed finite element approximation of this class of stochastic Keller--Segel systems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14390",
  "author_total": 1,
  "authors": [
    {
      "name": "Liet Vo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7ft1tgy7rdxk0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14390",
  "fulltext_url": null,
  "id": "7ft1tgy7rdxk0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14390",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "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": "W7221776153",
  "pdf_url": "https://arxiv.org/pdf/2610.14390",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7ft1tgy7rdxk0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.14390",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14390"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Optimal strong convergence of a splitting mixed finite element method for a stochastic Keller--Segel system",
  "title_text": "Optimal strong convergence of a splitting mixed finite element method for a stochastic Keller--Segel system",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/7ft1tgy7rdxk0",
  "venue": "arXiv",
  "versions": []
}