{
  "abstract": "Past work with Tom Seidman analyzed the spatial convergence order of the numerical finite element method applied to time-dependent diffusion-reaction equations with a measure-valued source term. For smooth source terms, the numerical method has second-order accuracy, but the non-smooth source terms introduce a limitation of the order that depends on the spatial dimension. This work in honor of Tom extends the analysis to the finite volume method in its clas- sical two-point flux form and shows that the regularity of the source term reduces the convergence order to 1 in two and 0.5 in three spatial dimensions which is reduced from the nominal second-order and depends on the space dimension. Computational tests with a point source modeled by a Dirac delta distribution exhibit the behavior predicted by the analytical results.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22063",
  "author_total": 4,
  "authors": [
    {
      "name": "Matthias Gobbert"
    },
    {
      "name": "Martin Kruž\\'ık"
    },
    {
      "name": "Andreas Meister"
    },
    {
      "name": "Michael Muscedere"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8fb2e0e2vqs6j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22063",
  "fulltext_url": null,
  "id": "8fb2e0e2vqs6j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22063",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2206|Advanced Numerical Methods in Computational Mathematics"
    ]
  ],
  "openalex": "W7222760755",
  "pdf_url": "https://arxiv.org/pdf/2610.22063",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8fb2e0e2vqs6j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.22063",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22063"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Finite Volume Convergence for a Heat Equation with a Measure-Valued Source",
  "title_text": "Finite Volume Convergence for a Heat Equation with a Measure-Valued Source",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/8fb2e0e2vqs6j",
  "venue": "arXiv",
  "versions": []
}