发表机构
Hunan Key Laboratory for Computation and Simulation in Science and Engineering, National Center for Applied Mathematics in Hunan, Xiangtan University（湘潭大学湖南省计算与模拟科学工程重点实验室国家应用数学中心（湖南））
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对线性应变梯度弹性问题，提出一种无需惩罚参数的稳定Morley有限元方法，利用离散Korn不等式保证鲁棒性，数值实验验证了理论。
AI 中文摘要
我们为满足二阶弱连续条件的有限元空间建立了离散的$H^1$-Korn不等式。这意味着经典的$H^2$-非协调元满足离散Korn不等式。基于此结果，我们仅使用分片二次多项式开发了一种稳定的Morley有限元方法，用于线性应变梯度弹性。得益于离散的$H^1$-Korn不等式，该方法不需要任何惩罚参数。我们证明了该方法对$\lambda$和$\iota$均具有鲁棒性。数值实验证实了理论结果。
英文摘要
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.
