{
  "abstract": "We consider a fractional diffusion problem with temporal nonlocality acting on the diffusive flux. A coercive space--time variational formulation in Bochner-valued fractional Sobolev spaces is derived and the existence, uniqueness, and regularity of solutions are established. We further develop a conforming tensor-product Galerkin discretization and prove quasi-optimal error estimates in the anisotropic energy norm and improved convergence rates in weaker norms using duality arguments. In contrast to some space-time formulations for classical diffusion, the method preserves the causal structure of the evolution problem and leads to a time-stepping procedure with memory terms. On uniform time grids, the discrete history operator has a lower-triangular Toeplitz structure which enables an efficient implementation using fast recursive convolution techniques.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00091",
  "author_total": 3,
  "authors": [
    {
      "name": "Herbert Egger"
    },
    {
      "name": "Marvin Fritz"
    },
    {
      "name": "Barbara Wohlmuth"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0y8gerrrgf3t6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00091",
  "fulltext_url": null,
  "id": "0y8gerrrgf3t6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00091",
  "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": "W7206154497",
  "pdf_url": "https://arxiv.org/pdf/2609.00091",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0y8gerrrgf3t6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.00091",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00091"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "A coercive space-time variational approach to fractional diffusion problems",
  "title_text": "A coercive space-time variational approach to fractional diffusion problems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/0y8gerrrgf3t6",
  "venue": "arXiv",
  "versions": []
}