{
  "abstract": "We develop a unified framework for high-order, fully discrete entropy-stable discontinuous Galerkin (DG) methods with compact explicit single-step time discretizations. At the end of each time step, the preliminary DG polynomial is scaled toward its cell average to enforce a strong cell entropy inequality while preserving conservation. This correction is feasible if and only if the updated cell average satisfies a weak cell entropy inequality, which standard third-order strong-stability-preserving Runge--Kutta DG updates can violate at arbitrarily small positive CFL numbers. For compact single-step schemes, including compact Runge--Kutta, Lax--Wendroff, and ADER-DG methods, we derive an explicit interval of feasible numerical entropy fluxes at each interface and prove that it is nonempty under a CFL condition. Projecting a compatible high-order target flux onto this interval guarantees the weak cell entropy inequality and preserves single-step high-order accuracy on smooth solutions, including near nondegenerate extrema. The limiter also enforces multiple entropy inequalities simultaneously. We also establish a Lax--Wendroff-type theorem. Numerical experiments for scalar conservation laws and the compressible Euler equations demonstrate high-order accuracy, multi-entropy control, and robustness for strong shocks.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30535",
  "author_total": 3,
  "authors": [
    {
      "name": "Yuchang Liu"
    },
    {
      "name": "Yan Jiang"
    },
    {
      "name": "Mengping Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eh09pmsetwy3a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30535",
  "fulltext_url": null,
  "id": "eh09pmsetwy3a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30535",
  "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|Computational Fluid Dynamics and Aerodynamics"
    ]
  ],
  "openalex": "W7223375229",
  "pdf_url": "https://arxiv.org/pdf/2610.30535",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eh09pmsetwy3a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.30535",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30535"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "High-Order Fully Discrete Entropy-Stable DG Methods with Compact Explicit Single-Step Time Discretizations",
  "title_text": "High-Order Fully Discrete Entropy-Stable DG Methods with Compact Explicit Single-Step Time Discretizations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/eh09pmsetwy3a",
  "venue": "arXiv",
  "versions": []
}