{
  "abstract": "We develop fully discrete multi-entropy-stable high-order compact Runge--Kutta discontinuous Galerkin (cRKDG) methods for hyperbolic conservation laws. Our main result is a weak cell entropy inequality for multi-dimensional systems after one full high-order Runge--Kutta (RK) time step. The proof exploits the cell-local intermediate stages of cRKDG: their perturbations are controlled by the initial in-cell variation. The analysis does not require a strong stability preserving decomposition or stagewise entropy correction. For a sufficiently dissipative Lax--Friedrichs flux and explicit RK methods with nonnegative output weights, the inequality holds under a suitable time-step restriction for strongly convex entropy pairs. For a prescribed, uniformly conditioned family of such entropies, common dissipation and time-step conditions ensure weak cell entropy stability for all entropy pairs. A single cell-average-preserving scaling at the end of each step then enforces all corresponding strong cell entropy inequalities simultaneously. We also prove a Lax--Wendroff-type theorem: under the stated assumptions, any strongly convergent sequence of numerical solutions converges to a weak solution satisfying all prescribed entropy inequalities. Numerical experiments in one and two dimensions demonstrate high-order accuracy, the benefit of multiple entropy constraints for nonconvex scalar problems, and robust performance on shock problems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18837",
  "author_total": 1,
  "authors": [
    {
      "name": "Zheng Sun"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bshj72dkx5bc4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18837",
  "fulltext_url": null,
  "id": "bshj72dkx5bc4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18837",
  "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": "W7221811391",
  "pdf_url": "https://arxiv.org/pdf/2610.18837",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bshj72dkx5bc4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:20Z",
      "native_id": "2610.18837",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18837"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Fully discrete multi-entropy-stable compact Runge--Kutta discontinuous Galerkin methods for hyperbolic conservation laws",
  "title_text": "Fully discrete multi-entropy-stable compact Runge--Kutta discontinuous Galerkin methods for hyperbolic conservation laws",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:20Z",
  "url": "https://research.draconitic.com/paper/bshj72dkx5bc4",
  "venue": "arXiv",
  "versions": []
}