{
  "abstract": "We develop a bihomotopy argument to estimate the discrete material time derivatives of consistency functionals. Combined with summation-by-parts, this argument yields a directional super-convergence estimate for the consistency contribution when tested with the normal error velocity. Together with the super-approximation of the reversely weighted discrete normal, these techniques establish $L_t^\\infty H_x^1$ super-convergence of the projection error and optimal $L_t^\\infty L_x^2$ convergence of the trajectory error of a stabilized BGN method for curve-shortening flow with piecewise linear parametric finite elements.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23326",
  "author_total": 1,
  "authors": [
    {
      "name": "Genming Bai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6x57zjebmytt0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23326",
  "fulltext_url": null,
  "id": "6x57zjebmytt0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23326",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2206|Advanced Numerical Methods in Computational Mathematics"
    ]
  ],
  "openalex": "W7214029535",
  "pdf_url": "https://arxiv.org/pdf/2609.23326",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6x57zjebmytt0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23326",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23326"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Super-approximation and optimal $L^2$ convergence of the stabilized BGN method with piecewise linear parametric finite elements for curve-shortening flow",
  "title_text": "Super-approximation and optimal L^2 convergence of the stabilized BGN method with piecewise linear parametric finite elements for curve-shortening flow",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/6x57zjebmytt0",
  "venue": "arXiv",
  "versions": []
}