{
  "abstract": "A second order finite difference scheme is analyzed for the nonlocal Cahn-Hilliard system with variable mobility and the singular Flory-Huggins logarithmic potential. The temporal discretization employs a modified Crank-Nicolson formulation, while the mobility is treated explicitly to guarantee ellipticity and reduce computational cost. To strictly enforce the positivity-preserving property at the discrete level, a nonlinear regularization term is added into the numerical scheme. Rigorous analysis shows that the scheme is uniquely solvable and stable under a modified numerical energy. The well-known analytical challenge associated with the variable mobility has to be handled carefully. To overcome this, a convergence framework is constructed based on two non-standard techniques: (1) a higher-order asymptotic expansion (extending up to the third order in time and fourth order in space) to retain a sufficiently order of accuracy; (2) a two-stage error strategy, wherein a rough error estimate first guarantees the discrete boundedness of the mobility and nonlinear terms, followed by a refined error analysis that yields the optimal convergence rate. Numerical experiments validate the theoretical results and demonstrate the robustness of the proposed scheme.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06092",
  "author_total": 2,
  "authors": [
    {
      "name": "Yuanyi Sheng"
    },
    {
      "name": "Zhengru Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f010p8pb4kedj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06092",
  "fulltext_url": null,
  "id": "f010p8pb4kedj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06092",
  "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",
      "2505|Solidification and crystal growth phenomena"
    ]
  ],
  "openalex": "W7212055271",
  "pdf_url": "https://arxiv.org/pdf/2609.06092",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f010p8pb4kedj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.06092",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06092"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "A Second Order Positivity-Preserving Scheme for the Nonlocal Cahn-Hilliard System with Variable Mobility and Logarithmic Flory-Huggins Potential",
  "title_text": "A Second Order Positivity-Preserving Scheme for the Nonlocal Cahn-Hilliard System with Variable Mobility and Logarithmic Flory-Huggins Potential",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/f010p8pb4kedj",
  "venue": "arXiv",
  "versions": []
}