Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Huang, Xuehai, Tang, Zheqian
Language: English
Subfield: Materials Chemistry
Field: Materials Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213602712