{
  "abstract": "The aim of the present study is to develop discontinuous Galerkin and nonconforming finite-element methods for solving the 2D advection-diffusion equation. The discrete formulations are stabilized by means of a family of numerical fluxes and the dispersion relations are constructed via a Fourier/stability analysis. The linear discontinuous P1DG and non conforming P1NC Galerkin discretizations are studied. A long time stability result is proven for the P1NC and P1DG schemes and fluxes examined here by inspecting the discrete frequencies, solutions of the dispersion relations. A super-convergent result is also demonstrated for the P1NC discrete frequency (O(h 4 ) accuracy) compared to the P1DG one (O(h 2 ) accuracy). These results are in line with those obtained in a previous paper for the shallow-water system.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29818",
  "author_total": 1,
  "authors": [
    {
      "name": "Daniel Y Le Roux"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1xfxfw7vexf6w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29818",
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  "id": "1xfxfw7vexf6w",
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  "landing_url": "https://hal.science/hal-05775566v1",
  "language": "en",
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  "metadata_licence": "CC0-1.0",
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      "2206|Advanced Numerical Methods in Computational Mathematics"
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  "openalex": "W7223214050",
  "pdf_url": "https://hal.science/hal-05775566/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1xfxfw7vexf6w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:46Z",
      "native_id": "hal-05775566",
      "source": "hal",
      "url": "https://hal.science/hal-05775566v1"
    },
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.29818",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29818"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "A super-convergent quasi-discontinuous Galerkin method for advection-diffusion problems",
  "title_text": "A super-convergent quasi-discontinuous Galerkin method for advection-diffusion problems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/1xfxfw7vexf6w",
  "venue": "HAL",
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