A Hybrid High-Order Method for the Elasticity Problem with Linear Slip Interface
Abstract
We design and analyse a hybrid high-order (HHO) method for the linear elasticity problem with a linear slip interface, i.e.\ with interface conditions of spring type, in which the jump of the displacement across the interface is proportional to the traction through a compliancy tensor bK=αbI+(β−α)udln⊗udln. The mesh is fitted to the interface, the discrete unknowns are polynomials of degree k≥ 1 on the mesh faces and of degree k+1 in the mesh cells, and general polytopal cells are allowed. The two novelties of the method lie in the local symmetric strain reconstruction, which incorporates the interface condition, and in the interface stabilisation, which is built from a regularised interface stiffness bSh in the spirit of Hansbo and Hansbo \cite{HH04}. As a consequence, a single formulation covers the whole range of compliancies, from the perfectly bonded interface α=β=0, where the interface stabilisation acts as a Nitsche-type penalty, to the traction-free interface obtained as α,β→+∞, and no unknown is attached to the jump. We prove that the discrete bilinear form is coercive and that the errors converge as hk+1 in the energy norm and as hk+2 in the L2 norm, with constants that are independent of the compliancy parameters and of the Lamé coefficient λ, so that the method is also locking free. Various numerical examples and comparisons are provided to confirm the theoretical results.
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BibTeX
@misc{burman2026hybrid,
title = {{A Hybrid High-Order Method for the Elasticity Problem with Linear Slip Interface}},
author = {Erik Burman and Peiqi Huang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20444},
eprint = {2609.20444},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20444},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Hybrid High-Order Method for the Elasticity Problem with Linear Slip Interface
AU - Erik Burman
AU - Peiqi Huang
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.20444
UR - https://arxiv.org/abs/2609.20444
AB - We design and analyse a hybrid high-order (HHO) method for the linear elasticity problem with a linear slip interface, i.e.\ with interface conditions of spring type, in which the jump of the displacement across the interface is proportional to the traction through a compliancy tensor bK=αbI+(β−α)udln⊗udln. The mesh is fitted to the interface, the discrete unknowns are polynomials of degree k≥ 1 on the mesh faces and of degree k+1 in the mesh cells, and general polytopal cells are allowed. The two novelties of the method lie in the local symmetric strain reconstruction, which incorporates the interface condition, and in the interface stabilisation, which is built from a regularised interface stiffness bS_h in the spirit of Hansbo and Hansbo \cite{HH04}. As a consequence, a single formulation covers the whole range of compliancies, from the perfectly bonded interface α=β=0, where the interface stabilisation acts as a Nitsche-type penalty, to the traction-free interface obtained as α,β→+∞, and no unknown is attached to the jump. We prove that the discrete bilinear form is coercive and that the errors converge as h^k+1 in the energy norm and as h^k+2 in the L^2 norm, with constants that are independent of the compliancy parameters and of the Lamé coefficient λ, so that the method is also locking free. Various numerical examples and comparisons are provided to confirm the theoretical results.
ER -