{
  "abstract": "In this work, we propose an unfitted finite element scheme to approximate the solution of the heat equation on moving domains. We use the ϕ-FEM paradigm in which the computational domain is described implicitly by a level-set function ϕ. This function is incorporated into the variational formulation in order to enforce the boundary conditions, which allows the use of unfitted meshes in space. Such a strategy avoids the need for remeshing at each time step and makes it possible to handle complex geometrical evolutions. Moreover, the ϕ-FEM approach has the advantage of being simple to implement within standard finite element libraries. We introduce a fully discrete scheme that combines the ϕ-FEM spatial discretization with the lowest-order discontinuous Galerkin method in time. Under regularity assumptions on the level-set function and a mild restriction linking the time step to the mesh size, we establish an optimal a priori error estimate in the L2(0,T;H1) norm. Finally, we present several numerical experiments that confirm this convergence rate, exhibit a second-order convergence in the L{\\infty}(0,T;L2) norm, and illustrate the robustness and accuracy of the proposed method.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15630",
  "author_total": 4,
  "authors": [
    {
      "name": "Michel Duprez"
    },
    {
      "name": "Johan Marguet"
    },
    {
      "name": "Alexei Lozinski"
    },
    {
      "name": "Igor Voulis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8mbh671fr92cz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15630",
  "fulltext_url": null,
  "id": "8mbh671fr92cz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15630",
  "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",
      "2206|Advanced Numerical Methods in Computational Mathematics"
    ]
  ],
  "openalex": "W7213309438",
  "pdf_url": "https://arxiv.org/pdf/2609.15630",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8mbh671fr92cz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.15630",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15630"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "A ϕ-FEM approach for time-dependent domains with unfitted meshes",
  "title_text": "A ϕ-FEM approach for time-dependent domains with unfitted meshes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/8mbh671fr92cz",
  "venue": "arXiv",
  "versions": []
}