In this paper, we develop two fully nonconforming (both H(grad curl)-nonconforming and H(curl)-nonconforming) finite elements on cubical meshes which can fit into the Stokes complex. The newly proposed elements have 24 and 36 degrees of freedom, respectively. Different from the fully H(grad curl)-nonconforming tetrahedral finite elements in [9], the elements in this paper lead to a robust finite element method to solve the singularly perturbed quad-curl problem. To confirm this, we prove the optimal convergence of order $O(h)$ for a fixed parameter $\epsilon$ and the uniform convergence of order $O(h^{1/2})$ for any value of $\epsilon$. Some numerical examples are used to verify the correctness of the theoretical analysis.

翻译：在本文中,我们开发了两种完全不兼容的元素(H(qrod curl)-不对齐和H(curl)-不对齐)-限制元素,这些元素可适用于斯托克斯综合体。新提议的元素分别具有24和36度的自由度。不同于[9]中完全H(grad curl)-不兼容的四面有限元素[9],本文件中的元素导致一种强有力的有限元素方法,以解决单孔径直的二次曲线问题。为了证实这一点,我们证明固定参数$(h) 的订单是最佳的趋同值。对于任何值为$(h ⁇ 1/2)的任何值来说,则统一了$(h ⁇ 1/2}) 的订单。一些数字例子用于核实理论分析的正确性。