{
  "abstract": "We propose a fully discrete method for linear fourth-order parabolic equations with Dirichlet boundary conditions, combining an implicit LBRFD multistep scheme in time with a mixed interior penalty discontinuous Galerkin (IPDG) method in space. The temporal discretization employs equispaced linear barycentric rational interpolants and incorporates a startup procedure. To facilitate the spatial discretization, the original problem is reformulated through an auxiliary variable. For certain parameter pairs $(n,d)$, the LBRFD method is shown to be $A(α)$-stable and to possess a wider stability angle than the corresponding BDF$p$ method of the same order. Stability and a priori error estimates are established via a $G$-energy technique and the discrete Grönwall lemma. The theoretical analysis yields a total $L^2$ error estimate of order $h^{k-1}+τ^p$, where $p=d$ if $n-d$ is even and $p=d+1$ if $n-d$ is odd. The reduced spatial convergence rate is attributed to boundary contributions on $\\partialΩ$. Despite this theoretical prediction, numerical experiments confirm the stability and demonstrate optimal convergence of order $h^{k+1}+τ^p$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.19250",
  "author_total": 3,
  "authors": [
    {
      "name": "Hongying Huang"
    },
    {
      "name": "Hong Zhang"
    },
    {
      "name": "Yanming Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9911e2crma8wc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.19250",
  "fulltext_url": null,
  "id": "9911e2crma8wc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.19250",
  "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": "W7203888768",
  "pdf_url": "https://arxiv.org/pdf/2608.19250",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9911e2crma8wc.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2608.19250",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.19250"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "A fully discrete LBRFD-IPDG method for linear fourth-order parabolic equations",
  "title_text": "A fully discrete LBRFD-IPDG method for linear fourth-order parabolic equations",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:42Z",
  "url": "https://research.draconitic.com/paper/9911e2crma8wc",
  "venue": "arXiv",
  "versions": []
}