{
  "abstract": "We establish a discrete $H^1$-Korn inequality for finite element spaces satisfying a second order weak continuity condition. This implies that classical $H^2$-nonconforming elements satisfy the discrete Korn inequality. Based on this result, we develop a stabilized Morley finite element method for linear strain gradient elasticity using only piecewise quadratic polynomials. Thanks to the discrete $H^1$-Korn inequality, this method does not require any penalty parameter. We prove that the method is robust with respect to both $λ$ and $ι$. Numerical experiments confirm the theoretical results.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24340",
  "author_total": 3,
  "authors": [
    {
      "name": "Xiao Li"
    },
    {
      "name": "Shudan Tian"
    },
    {
      "name": "Hua Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0rea3m9tpg2ah.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24340",
  "fulltext_url": null,
  "id": "0rea3m9tpg2ah",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24340",
  "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",
      "2505|Nonlocal and gradient elasticity in micro/nano structures"
    ]
  ],
  "openalex": "W7214035611",
  "pdf_url": "https://arxiv.org/pdf/2609.24340",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0rea3m9tpg2ah.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.24340",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24340"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Morley element for the linear strain gradient elasticity problem",
  "title_text": "Morley element for the linear strain gradient elasticity problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/0rea3m9tpg2ah",
  "venue": "arXiv",
  "versions": []
}