{
  "abstract": "We develop an incidence-based edge-averaged method for scalar convection-diffusion problems on convex polytopal meshes in arbitrary dimensions. The proposed method extends the classical edge-averaged finite-element scheme through a graph-theoretic formulation based on vertex-edge incidence matrices. We first establish this formulation on simplices in arbitrary dimensions and then extend it to convex polytopes by introducing complementary edges and generalized barycentric coordinates. A key ingredient is a matrix identity that relates the generalized Whitney edge mass matrix to a diagonal representation of the Poisson stiffness matrix, enabling an exponentially-fitted discretization expressed entirely in terms of nodal values and edge weights. We prove that the resulting stiffness matrix is a nonsingular $M$-matrix under suitable positivity and connectivity conditions, ensuring monotonicity and the discrete maximum principle. Numerical experiments on two- and three-dimensional simplicial and nonsimplicial meshes demonstrate first-order convergence in the $H^1$ semi-norm and stable, nonoscillatory solutions in convection-dominated regimes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01175",
  "author_total": 4,
  "authors": [
    {
      "name": "James H. Adler"
    },
    {
      "name": "Xiaozhe Hu"
    },
    {
      "name": "Seulip Lee"
    },
    {
      "name": "Eoghan O'Keefe"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1ye89ykgw9h57.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01175",
  "fulltext_url": null,
  "id": "1ye89ykgw9h57",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01175",
  "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.NA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01175",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1ye89ykgw9h57.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01175",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01175"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "An Incidence-Based Edge-Averaged Method for Convection-Diffusion Problems on Polytopal Meshes",
  "title_text": "An Incidence-Based Edge-Averaged Method for Convection-Diffusion Problems on Polytopal Meshes",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/1ye89ykgw9h57",
  "venue": "arXiv",
  "versions": []
}