{
  "abstract": "We propose and analyze an arbitrary-order globally divergence-free (GDF) discontinuous Galerkin (DG) method for the two-dimensional linear magnetic induction equation on unstructured triangular meshes. To the best of our knowledge, this is the first work to provide a rigorous energy-based analysis of high-order GDF-DG methods. First, we incorporate the edge normal-trace evolution into a closed, strictly local semidiscrete operator acting on the elementwise magnetic field alone. Then, we introduce two local modifications to the continuous electric field: a weighted patch moment correction that enforces local polynomial orthogonality and a vertex-patch stabilization that damps the remaining high-order modes. On shape-regular, quasi-uniform periodic triangulations, we prove semidiscrete energy stability with a sufficiently large mesh-independent penalty and establish a priori error estimates for smooth solutions. Numerical experiments support the analysis.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39299",
  "author_total": 3,
  "authors": [
    {
      "name": "Yuchang Liu"
    },
    {
      "name": "Yan Jiang"
    },
    {
      "name": "Mengping Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ffr6t8ht5tm7m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39299",
  "fulltext_url": null,
  "id": "ffr6t8ht5tm7m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39299",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39299",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ffr6t8ht5tm7m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39299",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39299"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Energy Stability and Error Estimates for a Globally Divergence-Free DG Method of Arbitrary Order",
  "title_text": "Energy Stability and Error Estimates for a Globally Divergence-Free DG Method of Arbitrary Order",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/ffr6t8ht5tm7m",
  "venue": "arXiv",
  "versions": []
}