{
  "abstract": "We develop a high-order fully discrete ALE-SAV finite element method for sharp-interface two-phase Navier--Stokes flow that satisfies a discrete energy dissipation law. We introduce an SAV reformulation to ensure the stable treatment of the surface and gravitational potential energies, together with an energy-stable ALE transfer operator that controls the density-weighted kinetic energy across moving meshes. The resulting scheme is linear and satisfies a modified energy-dissipation inequality. Numerical experiments, including rising-bubble benchmarks, demonstrate the robustness of the method and confirm second-order convergence in time and arbitrarily high-order convergence in space.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35590",
  "author_total": 1,
  "authors": [
    {
      "name": "Shu Ma"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c8dq1svaxkpbe.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35590",
  "fulltext_url": null,
  "id": "c8dq1svaxkpbe",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35590",
  "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": "W7214804409",
  "pdf_url": "https://arxiv.org/pdf/2609.35590",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c8dq1svaxkpbe.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.35590",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35590"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "High-order energy diminishing ALE-SAV finite element methods for two-phase Navier--Stokes flow",
  "title_text": "High-order energy diminishing ALE-SAV finite element methods for two-phase Navier--Stokes flow",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/c8dq1svaxkpbe",
  "venue": "arXiv",
  "versions": []
}