{
  "abstract": "We analyze the combined discretization of singularly perturbed reaction-diffusion problems with perturbation parameter $\\varepsilon\\in (0,1]$ and with parametric, Gevrey-regular reaction term, by $hp$-Galerkin FE methods and by higher-order polynomial lattice rules. We establish $\\varepsilon$-robust algebraic convergence rates for the combined QMC $hp$-FEM approximation that are not subject to the curse of dimensionality (CoD) in the parametric reaction coefficient, and only limited by the sparsity and the $\\mathfrak{s}_{y}$-Gevrey regularity of the reaction coefficient expansion. On the interval $(-1,1)$, we establish an $\\varepsilon$-robust, root-exponential convergence rate $\\exp(-σ\\, p_{\\mathrm{FE}}^{1/\\mathfrak{s}_{x}})$ for $hp$-Galerkin FEM for reaction-diffusion problems under $\\mathfrak{s}_{x}$-Gevrey regularity assumptions on the reaction coefficient and the source term, a result that can be of independent interest. Numerical experiments are consistent with the theoretical bounds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39738",
  "author_total": 2,
  "authors": [
    {
      "name": "Fabian Rohner"
    },
    {
      "name": "Christoph Schwab"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dr4eqep01g0hq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39738",
  "fulltext_url": null,
  "id": "dr4eqep01g0hq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39738",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39738",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dr4eqep01g0hq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39738",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39738"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Higher-Order QMC $hp$-FEM UQ for Singular Perturbation: Reaction-Diffusion with Gevrey-Parametric Reaction Coefficient",
  "title_text": "Higher-Order QMC hp-FEM UQ for Singular Perturbation: Reaction-Diffusion with Gevrey-Parametric Reaction Coefficient",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/dr4eqep01g0hq",
  "venue": "arXiv",
  "versions": []
}