{
  "abstract": "We construct and analyze a fully discrete finite volume scheme for the time-fractional Allen-Cahn equation with nondegenerate state-dependent mobility. The scheme combines a standard two-point flux approximation of diffusion, the L1 approximation of the Caputo derivative on a uniform time grid, and a semiconvex splitting of the potential, and it discretizes the inverse mobility by a secant average multiplying the entire L1 derivative. The key estimate is a lower bound for the accumulated pairing of this weighted L1 derivative with the solution increments in terms of the accumulated L1 quadratic form. Using this lower bound, we derive a discrete energy estimate and the time regularity required for compactness. For twice continuously differentiable semiconvex potentials satisfying sign conditions outside $(-1,1)$ and initial data in $H^1(Ω)$ taking values in $[-1,1]$, we prove existence of at least one fully discrete solution on every admissible finite volume mesh and every uniform time grid. Every such solution satisfies the maximum bound principle and a discrete energy bound relative to the initial energy, without a time-step restriction. In up to three space dimensions, under a mesh regularity condition with a constant independent of the mesh size, we prove that any sequence of fully discrete solutions has a subsequence converging strongly in $L^2(Ω\\times(0,T))$ to a weak solution of the continuous problem as the mesh size and time step tend to zero. As a consequence, we obtain existence of a weak solution in one and two space dimensions, and in three dimensions whenever such meshes exist.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00837",
  "author_total": 2,
  "authors": [
    {
      "name": "Yonghyeon Jeon"
    },
    {
      "name": "Kiwoong Kwon"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0gcjvbraav1kw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00837",
  "fulltext_url": null,
  "id": "0gcjvbraav1kw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00837",
  "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.AP"
    ],
    [
      "arxiv",
      "math.NA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00837",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0gcjvbraav1kw.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00837",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00837"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "A structure-preserving finite volume scheme for the time-fractional Allen-Cahn equation with nondegenerate state-dependent mobility",
  "title_text": "A structure-preserving finite volume scheme for the time-fractional Allen-Cahn equation with nondegenerate state-dependent mobility",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/0gcjvbraav1kw",
  "venue": "arXiv",
  "versions": []
}