{
  "abstract": "The fictitious domain method offers a powerful alternative to circumvent complex mesh generation process by embedding the complex physical domain into a simpler, non-matching background mesh. Among the various strategies to enforce the boundary condition on such a mesh, one possibility is to impose it weakly through a Lagrange multiplier. Existing approaches following this strategy typically require two independent uniform meshes for the domain and the boundary, whose mesh sizes are related by a prescribed ratio. In this work, we relax this requirement by constructing the boundary mesh directly from the trace of the background triangulation. To recover the uniform discrete inf-sup condition under this weaker mesh assumption, we enrich the discrete space of the solution with bubble functions. Our main result is the construction of a suitable operator that allows us to prove this uniform discrete inf-sup condition, thereby establishing the stability of the resulting scheme. As a consequence, we derive optimal a priori error estimates and provide a numerical experiment to validate the theoretical results.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19836",
  "author_total": 4,
  "authors": [
    {
      "name": "Stefano Berrone"
    },
    {
      "name": "Lorenzo Neva"
    },
    {
      "name": "Stefano Scialò"
    },
    {
      "name": "Fabio Vicini"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ewy4h6jhnqwg0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19836",
  "fulltext_url": null,
  "id": "ewy4h6jhnqwg0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19836",
  "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|Advanced Numerical Methods in Computational Mathematics"
    ]
  ],
  "openalex": "W7213610694",
  "pdf_url": "https://arxiv.org/pdf/2609.19836",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ewy4h6jhnqwg0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.19836",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19836"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "A Fictitious Domain Formulation with Bubble Enrichment",
  "title_text": "A Fictitious Domain Formulation with Bubble Enrichment",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/ewy4h6jhnqwg0",
  "venue": "arXiv",
  "versions": []
}