六阶椭圆型奇异摄动问题的鲁棒最优方法
A robust and optimal method for a sixth-order elliptic singular perturbation problem
AI总结：
本文针对含小参数的梯度弹性基尔霍夫板模型，提出一种无需稳定项、对参数鲁棒且h阶一致收敛的非协调有限元方法，通过数值实验验证了理论结果。
AI中文摘要：
本文针对含小参数0<ι<1的梯度弹性基尔霍夫板（GEKP）模型，提出一种鲁棒非协调有限元方法。该方法在离散空间采用H³三次有限元，在双线性形式的低阶项和右端项中采用插值映射至H²非协调有限元空间。值得注意的是，该数值方法对参数ι具有鲁棒性，无需任何稳定项即可达到h阶一致收敛。最后，开展了一些数值实验以验证理论结果。
英文摘要：
In this paper we propose a robust nonconforming finite method for a gradient-elastic Kirchhoff plate (GEKP) model with a small parameter $0<ι<1$. While the method employs an $H^3$ cubic finite element for the discrete space, it employs an interpolation mapping into an $H^2$ nonconforming finite element space in both the lower-order terms of the bilinear form and the right-hand side. Notably, the numerical method is robust with respect to the parameter $ι$ and uniformly convergent to order $h$ without any stabilized terms. Finally, some numerical experiments are performed to verify the theoretical findings.
