{
  "abstract": "We propose a vanishing-viscosity minimizing movement (VVMM) Fourier spectral method for scalar hyperbolic conservation laws under periodic boundary conditions. The method is a fully discrete space--time residual-minimizing scheme, Fourier spectral in space and polynomial in time, stabilized by vanishing viscosity and heat-kernel postprocessing. A basic analytical difficulty in Fourier discretizations of nonlinear conservation laws is the interaction between Fourier projection and the nonlinear flux; the resulting projection residual contains unresolved high-frequency components. VVMM addresses this issue by selecting, on each time slab, the numerical solution that minimizes {a penalized cut-off viscous conservation laws residual} and then applies heat-kernel postprocessing to damp unresolved modes. We prove a fully discrete $L^1$ error estimate, in any fixed space dimension, that separates the vanishing-viscosity error, the temporal interpolation error, and the spatial Fourier truncation error. {Under exact minimization of the penalized cut-off residual and suitable parameter coupling,} the estimate yields, for each fixed $γ>0$, an $L^1$ convergence rate $N^{-1/2+γ}$, with a constant depending on $γ$. Numerical experiments in one and two dimensions illustrate stable shock capturing without visible Gibbs oscillations and convergence behavior consistent with the theory.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30876",
  "author_total": 3,
  "authors": [
    {
      "name": "Lun Ji"
    },
    {
      "name": "Buyang Li"
    },
    {
      "name": "Fangyan Yao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/09c23cgyqyhax.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30876",
  "fulltext_url": null,
  "id": "09c23cgyqyhax",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30876",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2206|Computational Fluid Dynamics and Aerodynamics"
    ]
  ],
  "openalex": "W7214589689",
  "pdf_url": "https://arxiv.org/pdf/2609.30876",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/09c23cgyqyhax.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.30876",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30876"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "A vanishing-viscosity minimizing movement Fourier spectral method for scalar conservation laws",
  "title_text": "A vanishing-viscosity minimizing movement Fourier spectral method for scalar conservation laws",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/09c23cgyqyhax",
  "venue": "arXiv",
  "versions": []
}