{
  "abstract": "This paper addresses the numerical solution of nearly incompressible linear elasticity boundary value problems and their associated eigenvalue problems. A mixed finite element formulation based on Mini element is proposed to circumvent the locking phenomenon that plagues standard low-order elements in the nearly incompressible limit. For the boundary value problem, we establish the well-posedness of mixed variational formulation and derive a priori error estimates that are uniform with respect to the Lamé constant $\\underlineλ$, thereby proving the method's locking-free property. For the eigenvalue problem, we develop an efficient non-nested augmented subspace algorithm designed within the mixed finite element framework. A comprehensive convergence analysis is provided for the discrete eigenvalue approximation and the proposed iterative solver, demonstrating that the convergence rates remain independent of $\\underlineλ$. Numerical experiments on both problems confirm the theoretical conclusions, showing optimal convergence rates and robustness as $\\underlineλ \\to \\infty$. The results validate the effectiveness of Mini element and proposed augmented subspace algorithm for reliable and efficient computation in the nearly incompressible regime.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03780",
  "author_total": 4,
  "authors": [
    {
      "name": "Zhijin Guan"
    },
    {
      "name": "Yue Feng"
    },
    {
      "name": "Hehu Xie"
    },
    {
      "name": "Chenguang Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/10ptvh9cdt9n6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03780",
  "fulltext_url": null,
  "id": "10ptvh9cdt9n6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03780",
  "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": "W7208718802",
  "pdf_url": "https://arxiv.org/pdf/2609.03780",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/10ptvh9cdt9n6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2609.03780",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03780"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Mini mixed finite element method for nearly incompressible linear elasticity problems",
  "title_text": "Mini mixed finite element method for nearly incompressible linear elasticity problems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/10ptvh9cdt9n6",
  "venue": "arXiv",
  "versions": []
}