{
  "abstract": "We study a time fractional convection-diffusion-reaction equation in a bounded domain $Ω\\subset\\mathbb{R}^2$. A stabilized numerical scheme satisfying a discrete maximum principle is constructed by combining the conforming linear finite element method with the algebraic flux correction method. The resulting semi-discrete scheme is nonlinear, and its well-posedness is established. Assuming nonsmooth initial data, we derive error estimates for the semi-discrete scheme using energy arguments. For the temporal discretization, we employ the L1 method, obtaining a fully discrete scheme for which we prove well-posedness and the discrete maximum principle. We also present numerical experiments that validate the order of convergence as well as we test our schemes to solutions that possess layers.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03808",
  "author_total": 1,
  "authors": [
    {
      "name": "Christos Pervolianakis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/55nyt6n90mkj2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03808",
  "fulltext_url": null,
  "id": "55nyt6n90mkj2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03808",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2611|Fractional Differential Equations Solutions"
    ]
  ],
  "openalex": "W7208767391",
  "pdf_url": "https://arxiv.org/pdf/2609.03808",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/55nyt6n90mkj2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2609.03808",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03808"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "A stabilized scheme satisfying the discrete maximum principle for a time fractional convection-diffusion-reaction equation",
  "title_text": "A stabilized scheme satisfying the discrete maximum principle for a time fractional convection-diffusion-reaction equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/55nyt6n90mkj2",
  "venue": "arXiv",
  "versions": []
}