An interior penalty nonconforming finite element method for strain gradient elasticity
Abstract
An interior penalty nonconforming finite element method is developed for a strain gradient elasticity (SGE) model in arbitrary dimensions, using an H1-nonconforming displacement element built from vector-valued quadratic polynomials enriched by divergence-free face bubbles. Rigorous analysis establishes optimal and robust error estimates with respect to both the Lamé coefficient λ and the size parameter ι. The underlying divergence-commuting structure further leads to nonconforming finite element Stokes complexes in two and three dimensions. Numerical experiments support the predicted convergence behavior and parameter robustness, while a circular-hole benchmark under uniaxial tension illustrates the applicability of the method to a multiply connected domain.
Related
- Morley element for the linear strain gradient elasticity problem
- A Hybridized Staggered Discontinuous Galerkin--Mixed Finite Element Method for Strain Gradient Elasticity
- A nonoverlapping spectral additive Schwarz method for interior penalty discontinuous Galerkin discretizations of Anisotropic Elliptic Problems
- Polytopic symmetric interior-penalty approximation of elliptic SPDEs driven by spatial white noise
- A hybridization-derived interior penalty Nitsche method for heterogeneous and anisotropic diffusion
BibTeX
@misc{huang2026interior,
title = {{An interior penalty nonconforming finite element method for strain gradient elasticity}},
author = {Xuehai Huang and Zheqian Tang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19567},
eprint = {2609.19567},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19567},
}
RIS
TY - UNPB
TI - An interior penalty nonconforming finite element method for strain gradient elasticity
AU - Xuehai Huang
AU - Zheqian Tang
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.19567
UR - https://arxiv.org/abs/2609.19567
AB - An interior penalty nonconforming finite element method is developed for a strain gradient elasticity (SGE) model in arbitrary dimensions, using an H^1-nonconforming displacement element built from vector-valued quadratic polynomials enriched by divergence-free face bubbles. Rigorous analysis establishes optimal and robust error estimates with respect to both the Lamé coefficient λ and the size parameter ι. The underlying divergence-commuting structure further leads to nonconforming finite element Stokes complexes in two and three dimensions. Numerical experiments support the predicted convergence behavior and parameter robustness, while a circular-hole benchmark under uniaxial tension illustrates the applicability of the method to a multiply connected domain.
ER -