{
  "abstract": "An interior penalty nonconforming finite element method is developed for a strain gradient elasticity (SGE) model in arbitrary dimensions, using an $H^1$-nonconforming displacement element built from vector-valued quadratic polynomials enriched by divergence-free face bubbles. Rigorous analysis establishes optimal and robust error estimates with respect to both the Lamé coefficient $λ$ and the size parameter $ι$. The underlying divergence-commuting structure further leads to nonconforming finite element Stokes complexes in two and three dimensions. Numerical experiments support the predicted convergence behavior and parameter robustness, while a circular-hole benchmark under uniaxial tension illustrates the applicability of the method to a multiply connected domain.",
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  "article_type": null,
  "arxiv": "2609.19567",
  "author_total": 2,
  "authors": [
    {
      "name": "Xuehai Huang"
    },
    {
      "name": "Zheqian Tang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7atd65xd99kcm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19567",
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  "id": "7atd65xd99kcm",
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  "landing_url": "https://arxiv.org/abs/2609.19567",
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  "metadata_licence": "CC0-1.0",
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    [
      "arxiv",
      "cs.NA"
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      "arxiv",
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      "openalex",
      "2505|Nonlocal and gradient elasticity in micro/nano structures"
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  "openalex": "W7213602712",
  "pdf_url": "https://arxiv.org/pdf/2609.19567",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7atd65xd99kcm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.19567",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19567"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
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  ],
  "title": "An interior penalty nonconforming finite element method for strain gradient elasticity",
  "title_text": "An interior penalty nonconforming finite element method for strain gradient elasticity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/7atd65xd99kcm",
  "venue": "arXiv",
  "versions": []
}