{
  "abstract": "We develop a multilevel Monte Carlo framework for coercive elliptic problems with random diffusion and reaction coefficients on polytopic meshes, with particular emphasis on the approximation and inter-level coupling of random coefficients generated from spatially represented latent fields. The main analytical contribution is a Strang-type error decomposition in a DG norm that separates the forward discretisation error from the error introduced by approximating the random coefficients. On this basis, we study two coefficient-generation and multilevel-coupling strategies, a spectral sampler based on a stationary Gaussian latent field defined on a fixed Cartesian reference grid, and an SPDE-based Matérn sampler in which levels are coupled through projected white-noise loads on agglomerated hierarchies. Both fit into the same coefficient-aware analytical framework and couple adjacent levels directly through a common latent random input. The theory is supported by numerical experiments on general Voronoi and agglomerated polytopic meshes, demonstrating the predicted forward and coefficient-representation errors, decay of multilevel corrections, strong inter-level coupling, and the resulting work-accuracy behaviour relative to single-level Monte Carlo.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31861",
  "author_total": 4,
  "authors": [
    {
      "name": "Veronika Chronholm"
    },
    {
      "name": "Matt Evans"
    },
    {
      "name": "Emmanuil H. Georgoulis"
    },
    {
      "name": "Tristan Pryer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f0500bw4ze33e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31861",
  "fulltext_url": null,
  "id": "f0500bw4ze33e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31861",
  "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",
      "1804|Probabilistic and Robust Engineering Design"
    ]
  ],
  "openalex": "W7223694751",
  "pdf_url": "https://arxiv.org/pdf/2610.31861",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f0500bw4ze33e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.31861",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31861"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Multilevel Monte Carlo for Polytopic DG Discretisations with Spatially Represented Random Coefficients",
  "title_text": "Multilevel Monte Carlo for Polytopic DG Discretisations with Spatially Represented Random Coefficients",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/f0500bw4ze33e",
  "venue": "arXiv",
  "versions": []
}