{
  "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 \\emph{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∞(0,T;L2) norm, and illustrate the robustness and accuracy of the proposed method.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 4,
  "authors": [
    {
      "name": "Michel Duprez"
    },
    {
      "name": "Johan Marguet"
    },
    {
      "name": "Alexei Lozinski"
    },
    {
      "name": "Igor Voulis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4q8777e5sx5qn.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "4q8777e5sx5qn",
  "issns": [],
  "landing_url": "https://hal.science/hal-05749443v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-ap"
    ],
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      "1.math.math-na"
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  "openalex": null,
  "pdf_url": "https://hal.science/hal-05749443/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4q8777e5sx5qn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:34Z",
      "native_id": "hal-05749443",
      "source": "hal",
      "url": "https://hal.science/hal-05749443v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-ap",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-na",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-oc",
      "subfield": "optimisation-control"
    }
  ],
  "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": "2026-10-30T12:17:34Z",
  "url": "https://research.draconitic.com/paper/4q8777e5sx5qn",
  "venue": "HAL",
  "versions": []
}