{
  "abstract": "This paper studies numerical methods for the time fractional diffusion-wave equations with the constant delay. Using a symmetric fractional-order reduction technique and introducing the auxiliary variable $w$, we reformulate the original problem as an equivalent coupled system and for the first time carry out a rigorous regularity analysis of $w$. Based on the symmetric graded time mesh, the coupled problem is discretised by the $L1$ scheme in time and a standard finite element method in space, and the stability result of the developed fully discrete finite element scheme is established by means of a discrete fractional Grönwall inequality. Furthermore, we derive a new comparison principle and reconstruct a new barrier function on each interval $((k-1)τ,kτ]$, $1\\le k\\le K$ according to the properties of the symmetric graded mesh. Based on the new barrier function, we obtain new relevant properties, which lead to a novel and crucial stability property for the discrete fractional operator. Combining the obtained local truncation error in time gives a local error estimate for the fully discrete finite element scheme, which shows that our convergence result provides a unified framework that seamlessly encompasses both pointwise-in-time error estimates on uniform meshes and global-in-time error estimates on symmetrical graded meshes. Numerical experiments confirm the theoretical results.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21056",
  "author_total": 4,
  "authors": [
    {
      "name": "Xuan Li"
    },
    {
      "name": "Kaile Qiu"
    },
    {
      "name": "Chaobao Huang"
    },
    {
      "name": "Weiping Bu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a7v3ermqe56w3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21056",
  "fulltext_url": null,
  "id": "a7v3ermqe56w3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21056",
  "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",
      "2611|Fractional Differential Equations Solutions"
    ]
  ],
  "openalex": "W7222436052",
  "pdf_url": "https://arxiv.org/pdf/2610.21056",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a7v3ermqe56w3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21056",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21056"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Galerkin finite element method for time fractional diffusion-wave equations with constant time delay",
  "title_text": "Galerkin finite element method for time fractional diffusion-wave equations with constant time delay",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/a7v3ermqe56w3",
  "venue": "arXiv",
  "versions": []
}