An Unfitted Hybrid High-Order Method for the Elastodynamics Problem with Imperfect Interface
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=αbI+(β−α)bn⊗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 bSh=(hTδ−1bI+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 hk+1 and an L2-error estimate of order hk+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∈{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.
Related
- A Localized Hybrid Finite Element--Random Feature Method for Elliptic Interface Problems on Unfitted Meshes
- On an inverse boundary problem in elastodynamics
- Geometry-Conforming Finite Element Methods for Interface Problems on Fitted and Unfitted Meshes
- A Hybrid High-Order Method for the Elasticity Problem with Linear Slip Interface
- The conductivity problem with imperfect bonding interfaces and finite internal conductivities
BibTeX
@misc{huang2026unfitted,
title = {{An Unfitted Hybrid High-Order Method for the Elastodynamics Problem with Imperfect Interface}},
author = {Peiqi Huang and Erik Burman},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01504},
eprint = {2610.01504},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01504},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An Unfitted Hybrid High-Order Method for the Elastodynamics Problem with Imperfect Interface
AU - Peiqi Huang
AU - Erik Burman
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01504
UR - https://arxiv.org/abs/2610.01504
AB - 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=αbI+(β−α)bn⊗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^−1bI+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∈{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.
ER -