{
  "abstract": "We prove the convergence of the isoparametric Barrett--Garcke--Nürnberg (BGN) method for mean curvature flow of closed surfaces. For finite elements of degree $k\\ge6$ and time steps $τ=O(h^2)$, the numerical surfaces converge to the exact surfaces in the manifold distance with order $h^2$. The proof relies on two ingredients. First, we construct approximation flows by an expansion in time, whose interpolations satisfy the BGN method with an improved defect. Second, we derive a refined estimate for the tangential error from an algebraic identity for tangential test functions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08972",
  "author_total": 1,
  "authors": [
    {
      "name": "Yifei Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/18akep7jdsq0n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08972",
  "fulltext_url": null,
  "id": "18akep7jdsq0n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08972",
  "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": "W7220892975",
  "pdf_url": "https://arxiv.org/pdf/2610.08972",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/18akep7jdsq0n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.08972",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08972"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Convergence of isoparametric BGN methods for mean curvature flow of closed surfaces with high-order finite elements",
  "title_text": "Convergence of isoparametric BGN methods for mean curvature flow of closed surfaces with high-order finite elements",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/18akep7jdsq0n",
  "venue": "arXiv",
  "versions": []
}