{
  "abstract": "We analyse a discontinuous Galerkin method for two-dimensional scalar conservation laws on curved domains. Small intersections of a Cartesian grid with the domain are combined by rectangular cell merging. The local space is the restriction of $\\mathbb Q_k$ to each physical merged cell. An entropy-conservative flux is supplemented by face viscosity and, for odd degrees, a skew derivative-jump correction on unmerged interior squares. We prove exact semidiscrete $L^2$ dissipation and an optimal error estimate for every fixed $k\\ge1$. For smooth solutions with homogeneous trace on the entire boundary, the semi-discrete method satisfies an $O(h^{k+1})$ error bound. The constants are independent of the original cut-cell area fractions. The proof combines a physical-cell $L^2$ projection and cancellation of regular-face projection errors. A separate semidiscrete result covers linear transport with upwind inflow data. Computations for Burgers' equation on a disk and linear advection on a smooth star exhibit orders close to $k+1$ for $k=1,2,3$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.32107",
  "author_total": 1,
  "authors": [
    {
      "name": "Yong Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/edewm2gyrq9ze.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.32107",
  "fulltext_url": null,
  "id": "edewm2gyrq9ze",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.32107",
  "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",
      "2206|Advanced Numerical Methods in Computational Mathematics"
    ]
  ],
  "openalex": "W7214794422",
  "pdf_url": "https://arxiv.org/pdf/2609.32107",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/edewm2gyrq9ze.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.32107",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.32107"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "A merged-cell discontinuous Galerkin method for scalar conservation laws on curved domains",
  "title_text": "A merged-cell discontinuous Galerkin method for scalar conservation laws on curved domains",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/edewm2gyrq9ze",
  "venue": "arXiv",
  "versions": []
}