{
  "abstract": "We propose a filtered time stepping finite element scheme for curve shortening flow of open and closed curves in arbitrary codimension that is second-order accurate in time. Open curves are assumed to evolve inside a given domain $Ω\\subset \\mathbb R^n$, $n\\geq2$, and meet the external boundary $\\partialΩ$ orthogonally. We prove optimal error bounds for the $L^2$-- and $H^1$--norms. In practice only a single linear system needs to be solved at each time step. Numerical experiments confirm the accuracy and practicality of the introduced method, including an asymptotic equidistribution property.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21871",
  "author_total": 2,
  "authors": [
    {
      "name": "Klaus Deckelnick"
    },
    {
      "name": "Robert Nürnberg"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1fzcwp95xj5m3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21871",
  "fulltext_url": null,
  "id": "1fzcwp95xj5m3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21871",
  "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": "W7213906878",
  "pdf_url": "https://arxiv.org/pdf/2609.21871",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1fzcwp95xj5m3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.21871",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21871"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "A filtered time stepping scheme for curve shortening flow for open and closed curves",
  "title_text": "A filtered time stepping scheme for curve shortening flow for open and closed curves",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/1fzcwp95xj5m3",
  "venue": "arXiv",
  "versions": []
}