{
  "abstract": "We analyze higher-order quasi-Monte Carlo (QMC) Galerkin discretizations for a singularly perturbed reaction-diffusion problem with an affine-parametric reaction coefficient. We derive error estimates that are robust with respect to the perturbation parameter $\\varepsilon$. To this end, we establish $\\varepsilon$-uniform stability and mixed-parametric regularity estimates in an $\\varepsilon$-weighted energy norm, with constants independent of the parameter dimension and of $\\varepsilon$. These estimates imply robust dimension truncation estimates and dimension-independent higher-order QMC error bounds for linear quantities of interest. Assuming an abstract, $\\varepsilon$-robust finite element approximation property, we combine the parametric estimates with the spatial discretization analysis to derive a general fully discrete QMC-FE error estimate with constants independent of both the parameter dimension and $\\varepsilon$. We verify this approximation property for a one-dimensional model problem using continuous piecewise affine finite elements on Shishkin meshes. Numerical experiments illustrate the predicted robustness and convergence rates.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39734",
  "author_total": 2,
  "authors": [
    {
      "name": "Fabian Rohner"
    },
    {
      "name": "Christoph Schwab"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bctgn5xxm893f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39734",
  "fulltext_url": null,
  "id": "bctgn5xxm893f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39734",
  "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/2610.39734",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bctgn5xxm893f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39734",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39734"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Higher-Order QMC Galerkin FEM for Singular Perturbation: Reaction-Diffusion with Affine-Parametric Reaction",
  "title_text": "Higher-Order QMC Galerkin FEM for Singular Perturbation: Reaction-Diffusion with Affine-Parametric Reaction",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/bctgn5xxm893f",
  "venue": "arXiv",
  "versions": []
}