{
  "abstract": "We propose an energy-stable arbitrary Lagrangian-Eulerian (ALE) finite element formulation for incompressible Navier-Stokes flows with surface-tension-driven free boundaries. The key ingredient is a multiplier-free compensated tangential velocity formulation, which redistributes boundary nodes via the discrete tangential curvature residual. The relaxation parameter governing the artificial tangential velocity is scaled according to the viscous-capillary balance, yielding the natural choice $α= γ_0/ μ$, where $γ_0$ is the surface tension coefficient and $μ$ is the dynamic viscosity. We prove that the fully discrete scheme is well-posed, energy-dissipative, and temporally consistent with its semi-discrete counterpart. Numerical results confirm the robustness of the proposed method across a range of $μ$ and $γ_0$ values. Furthermore, the method exhibits superior mesh quality preservation compared with the BGN method, particularly in the small-time-step regime.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09301",
  "author_total": 3,
  "authors": [
    {
      "name": "Nuo Lei"
    },
    {
      "name": "Weiying Zheng"
    },
    {
      "name": "Na Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ar55775tmt2ev.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09301",
  "fulltext_url": null,
  "id": "ar55775tmt2ev",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09301",
  "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",
      "2206|Advanced Numerical Methods in Computational Mathematics"
    ]
  ],
  "openalex": "W7220932476",
  "pdf_url": "https://arxiv.org/pdf/2610.09301",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ar55775tmt2ev.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.09301",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09301"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "An energy--stable ALE--FEM with compensated tangential velocity for Navier--Stokes free--boundary flows",
  "title_text": "An energy--stable ALE--FEM with compensated tangential velocity for Navier--Stokes free--boundary flows",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/ar55775tmt2ev",
  "venue": "arXiv",
  "versions": []
}