{
  "abstract": "We develop the first tensor-product sparse-grid finite element discretizations of Bernstein--Gelfand--Gelfand (BGG) complexes. Alpert wavelets and their first and second primitives yield compatible hierarchies of discontinuous, continuous, and continuously differentiable piecewise polynomials, that serve as one-dimensional ingredients of BGG sparse-grid finite elements. We construct a bounded commuting sparse-grid projection that yields stable discrete potentials for Hessian, elasticity, and div-div complexes. Under mixed Sobolev regularity, we prove sparse-grid approximation estimates with dimension-independent convergence rates in the number of degrees of freedom. Experiments for a three-dimensional incompatibility problem and a two-dimensional biharmonic problem on an annulus illustrate the efficiency of sparse grids relative to full grids.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29516",
  "author_total": 2,
  "authors": [
    {
      "name": "Yihanqi Hu"
    },
    {
      "name": "Yuwen Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/75t3td5n2agey.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29516",
  "fulltext_url": null,
  "id": "75t3td5n2agey",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29516",
  "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",
      "2206|Advanced Numerical Methods in Computational Mathematics"
    ]
  ],
  "openalex": "W7223212331",
  "pdf_url": "https://arxiv.org/pdf/2610.29516",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/75t3td5n2agey.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.29516",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29516"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Sparse-grid discretizations of BGG sequences",
  "title_text": "Sparse-grid discretizations of BGG sequences",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/75t3td5n2agey",
  "venue": "arXiv",
  "versions": []
}