{
  "abstract": "Second-order flows represent an emerging computational framework for approaching stationary points of variational energies, characterized by damped hyperbolic partial differential equations. In this paper, we develop a scalar auxiliary variable (SAV) method for this class of flows, referred to as SAV-E. The resulting scheme is linear and decoupled, and we prove unconditional modified-energy stability. We further establish subsequential convergence to stationary points for the Ginzburg-Landau and conserved Swift-Hohenberg models under suitable assumptions. Numerical experiments support the analysis and demonstrate robustness and efficiency compared with representative baselines and the corresponding gradient flows.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19884",
  "author_total": 4,
  "authors": [
    {
      "name": "Haifan Chen"
    },
    {
      "name": "Wei Liu"
    },
    {
      "name": "Ziqing Xie"
    },
    {
      "name": "Yifang Yuan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e8dcse4g15yxf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19884",
  "fulltext_url": null,
  "id": "e8dcse4g15yxf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19884",
  "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": "W7221867132",
  "pdf_url": "https://arxiv.org/pdf/2610.19884",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e8dcse4g15yxf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19884",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19884"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Second-Order Flows for Approaching Stationary Points via the SAV-E Approach",
  "title_text": "Second-Order Flows for Approaching Stationary Points via the SAV-E Approach",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/e8dcse4g15yxf",
  "venue": "arXiv",
  "versions": []
}