{
  "abstract": "We establish sharp strong error estimates for a fully discrete approximation of semilinear stochastic convection--diffusion equations driven by additive noise subject to nonsmooth initial data. The problem is discretized in space using a standard Galerkin finite element method and in time via the linearly implicit Euler scheme. By decoupling the noise regularity index $β\\in (0, 2]$ from the initial data regularity index $μ\\in (0, 2]$, we derive time-weighted spatial and temporal regularity bounds that isolate the initial singularity at $t = 0$ into an integrable temporal weight. By allowing the drift operator $F$ to map into negative-order fractional spaces to incorporate the convection term, we prove sharp strong convergence rates of order $O(h^β+ k^{β/2})$ for $β\\in (0, 2)$ and $O\\bigl(h^2 + k(1+\\ln(t_n/k))^{1/2}\\bigr)$ at the critical endpoint $β= 2$ for any fixed $t_n > 0$, without requiring the regularity of the initial data to match that of the noise. Furthermore, these convergence rates are achieved under a relaxed differentiability condition requiring only a Lipschitz continuous first Gâteaux derivative of $F$. Numerical experiments validate the theoretical results across both trace-class and space-time white noise regimes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.26797",
  "author_total": 2,
  "authors": [
    {
      "name": "Jitendra Nath Naik"
    },
    {
      "name": "Lok Pati Tripathi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fp3yq7psn6tq3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.26797",
  "fulltext_url": null,
  "id": "fp3yq7psn6tq3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.26797",
  "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": "W7171831849",
  "pdf_url": "https://arxiv.org/pdf/2607.26797",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fp3yq7psn6tq3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2607.26797",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.26797"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Sharp Error Estimates for a Fully Discrete Approximation of Semilinear Stochastic Convection--Diffusion Equations with Additive Noise and Nonsmooth Initial Data",
  "title_text": "Sharp Error Estimates for a Fully Discrete Approximation of Semilinear Stochastic Convection--Diffusion Equations with Additive Noise and Nonsmooth Initial Data",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/fp3yq7psn6tq3",
  "venue": "arXiv",
  "versions": []
}