{
  "abstract": "We develop an energy-stable variable-step BDF2-based scalar auxiliary variable (SAV) finite element scheme for a droplet thin-film coarsening model with a Lennard–Jones singular potential. The method uses continuous piecewise linear finite elements in space and retains the original linear SAV update. We prove discrete mass conservation, modified-energy decay under an admissible step-ratio condition, and solvability of the coupled algebraic system. A Sherman–Morrison realization exploits the rank-one coupling and reduces each accepted time step to two solves with the same sparse base matrix. Numerical experiments assess temporal and spatial convergence, SAV-shift sensitivity, two-droplet mesh dependence, long-time coarsening, and solver efficiency. The film-height variable exhibits second-order temporal convergence and the expected spatial rates, whereas the auxiliary variable is first-order accurate; the consistency audit shows no hidden cancellation. The computations also verify mass conservation, modified-energy decay, positive film heights in the reported runs, and the efficiency of the sparse solver.",
  "abstract_shown": true,
  "affiliations": [
    "School of Mathematics, Physics and Artificial Intelligence, China University of Petroleum-Beijing at Karamay, Karamay 834000, China",
    "School of Sciences, Lanzhou University of Technology, Lanzhou 730050, China",
    "School of Optoelectronics, University of Chinese Academy of Sciences, Beijing 100049, China",
    "Department of Mathematics, Faculty of Arts and Sciences, Beijing Normal University, Zhuhai 519087, China"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 4,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Maoqin Yuan"
    },
    {
      "affs": [
        1
      ],
      "name": "Juan Zhang"
    },
    {
      "affs": [
        2
      ],
      "name": "Mingyang Li",
      "orcid": "0009-0004-4315-9772"
    },
    {
      "affs": [
        3
      ],
      "name": "Lixiu Dong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7b3pt4ydnakd8.bib",
  "cited_by": 0,
  "doi": "10.3390/axioms15100751",
  "fulltext_url": null,
  "id": "7b3pt4ydnakd8",
  "issns": [
    "2075-1680"
  ],
  "landing_url": "https://www.mdpi.com/2075-1680/15/10/751",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2206|Advanced Numerical Methods in Computational Mathematics"
    ]
  ],
  "openalex": "W7221111634",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/7b3pt4ydnakd8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:30Z",
      "native_id": "10.3390/axioms15100751",
      "source": "crossref",
      "url": "https://www.mdpi.com/2075-1680/15/10/751"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "journal-openalex:F26",
      "subfield": "general"
    }
  ],
  "title": "An Energy-Stable Variable-Step SAV Finite Element Method for a Droplet Thin-Film Coarsening Model with a Lennard–Jones Singular Potential",
  "title_text": "An Energy-Stable Variable-Step SAV Finite Element Method for a Droplet Thin-Film Coarsening Model with a Lennard–Jones Singular Potential",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:30Z",
  "url": "https://research.draconitic.com/paper/7b3pt4ydnakd8",
  "venue": "Axioms",
  "versions": []
}