{
  "abstract": "We design and analyse an unfitted hybrid high-order (HHO) method for the elastic wave equation in a medium made of two components separated by an imperfect interface of linear slip type, across which the traction is continuous and the displacement jump is proportional to the traction through a compliancy tensor $\\bK=α\\bI+(β-α)\\bn\\otimes\\bn$. The mesh is not fitted to the interface: the discrete unknowns are doubled in the cut cells, the small cuts are cured by a cell agglomeration procedure, and no unknown is attached to the interface. The two specific ingredients of the method are a local symmetric strain reconstruction in each cut subcell, which incorporates the interface condition through the regularised interface stiffness $\\bS_h=(h_Tδ^{-1}\\bI+\\bK)^{-1}$ in the spirit of Hansbo and Hansbo {\\em{A finite element method for the simulation of strong and weak discontinuities in solid mechanics.}} {Comput. Methods Appl. Mech. Engrg.}, 193, 2004, and an interface stabilisation built from the same matrix. For the space semi-discrete problem we prove that the discrete bilinear form is coercive and continuous, and we derive an energy-error estimate of order $h^{k+1}$ and an $L^2$-error estimate of order $h^{k+2}$, with constants independent of the compliancy parameters and of how the interface cuts the mesh. The scheme is combined either with the Newmark scheme, which conserves a discrete energy exactly, or with singly diagonally implicit Runge--Kutta schemes of order up to four. Numerical experiments in two dimensions confirm the predicted convergence rates for $k\\in\\{1,2,3\\}$, the robustness with respect to the compliancy over sixteen orders of magnitude, and illustrate the propagation of elastic waves across an unresolved slipping interface.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01504",
  "author_total": 2,
  "authors": [
    {
      "name": "Peiqi Huang"
    },
    {
      "name": "Erik Burman"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/06dhaaedsj55n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01504",
  "fulltext_url": null,
  "id": "06dhaaedsj55n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01504",
  "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/2610.01504",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/06dhaaedsj55n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.01504",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01504"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "An Unfitted Hybrid High-Order Method for the Elastodynamics Problem with Imperfect Interface",
  "title_text": "An Unfitted Hybrid High-Order Method for the Elastodynamics Problem with Imperfect Interface",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/06dhaaedsj55n",
  "venue": "arXiv",
  "versions": []
}