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An Unfitted Hybrid High-Order Method for the Elastodynamics Problem with Imperfect Interface — arXiv:2610.01504

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.01504
License (as archived): CC0-1.0
Archived: 2026-10-06T17:37:47.652Z
SHA-256 of the archived text: 8108ad64555bb6fbc48d73f28549b9402bf4bbe6923f6617a69724f33d2c0d32
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How to cite

An Unfitted Hybrid High-Order Method for the Elastodynamics Problem with Imperfect Interface — arXiv:2610.01504 — arXiv (en), https://arxiv.org/abs/2610.01504 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_298cbbb2b2da (Metraipolis archive dc_298cbbb2b2da, sha256 8108ad64555bb6fbc48d73f28549b9402bf4bbe6923f6617a69724f33d2c0d32)

BibTeX

@misc{dc298cbbb2b2da,
  title = {An Unfitted Hybrid High-Order Method for the Elastodynamics Problem with Imperfect Interface — arXiv:2610.01504},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.01504},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_298cbbb2b2da; sha256 8108ad64555bb6fbc48d73f28549b9402bf4bbe6923f6617a69724f33d2c0d32},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.01504. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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 $\bK=\alpha\bI+(\beta-\alpha)\bn\otimes\bn$. 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 $\bS_h=(h_T\delta^{-1}\bI+\bK)^{-1}$ 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.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-10-02 in math.NA).
Categorie arXiv: Numerical Analysis (math.NA).
Pagina del lavoro: https://arxiv.org/abs/2610.01504 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-06T16:04:06.495Z dalla pagina https://arxiv.org/catchup/math.NA/2026-10-02?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).