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arXiv · 2609.24340

Morley element for the linear strain gradient elasticity problem

Xiao Li·Shudan Tian·Hua Wang
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Abstract

We establish a discrete $H^1$-Korn inequality for finite element spaces satisfying a second order weak continuity condition. This implies that classical $H^2$-nonconforming elements satisfy the discrete Korn inequality. Based on this result, we develop a stabilized Morley finite element method for linear strain gradient elasticity using only piecewise quadratic polynomials. Thanks to the discrete $H^1$-Korn inequality, this method does not require any penalty parameter. We prove that the method is robust with respect to both $λ$ and $ι$. Numerical experiments confirm the theoretical results.

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Xiao Li, Shudan Tian, Hua Wang. 2026-09-21. Morley element for the linear strain gradient elasticity problem. https://arxiv.org/abs/2609.24340

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