{
  "abstract": "The optimization-based cell average limiter enforces global conservation and bounds, and has been successfully applied to discontinuous Galerkin (DG) discretizations of a wide range of nonlinear systems, from phase-field models to the compressible Navier-Stokes equations. In this paper, taking the heat and convection-diffusion equations as prototypes, we analyze the convergence of the scheme resulting from cell average limiting. Encoding conservation and admissibility in a differential inclusion identifies the limiter as a backward Euler proximal step in a Lie splitting of the constrained evolution. This proximal step is the metric projection onto the convex admissible set, and we prove that it is nonexpansive and stable in the $L^2$ norm, and that it does not increase the total variation of the cell averages. Combined with the standard error analysis, nonexpansiveness yields an $O(τ+h^{k+1})$ estimate for implicit Euler time stepping with DG discretization of polynomial degree $k$ under a reverse CFL condition, together with an unconditional $O(τ+h^{k})$ estimate. Numerical experiments confirm the predicted convergence rates and the enforcement of the bounds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33449",
  "author_total": 3,
  "authors": [
    {
      "name": "Seungmin Lee"
    },
    {
      "name": "Sanghyun Lee"
    },
    {
      "name": "Chen Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bmgqwvjxhtbqg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33449",
  "fulltext_url": null,
  "id": "bmgqwvjxhtbqg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33449",
  "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",
      "2206|Advanced Numerical Methods in Computational Mathematics"
    ]
  ],
  "openalex": "W7223886534",
  "pdf_url": "https://arxiv.org/pdf/2610.33449",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bmgqwvjxhtbqg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.33449",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33449"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Optimization-based Cell Average Limiters as Metric Projections: Constrained Evolution and Convergence Analysis for Convection-diffusion Equations",
  "title_text": "Optimization-based Cell Average Limiters as Metric Projections: Constrained Evolution and Convergence Analysis for Convection-diffusion Equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/bmgqwvjxhtbqg",
  "venue": "arXiv",
  "versions": []
}