We propose two families of nonconforming elements on cubical meshes: one for the $-\text{curl}\Delta\text{curl}$ problem and the other for the Brinkman problem. The element for the $-\text{curl}\Delta\text{curl}$ problem is the first nonconforming element on cubical meshes. The element for the Brinkman problem can yield a uniformly stable finite element method with respect to the parameter $\nu$. The lowest-order elements for the $-\text{curl}\Delta\text{curl}$ and the Brinkman problems have 48 and 30 degrees of freedom, respectively. The two families of elements are subspaces of $H(\text{curl};\Omega)$ and $H(\text{div};\Omega)$, and they, as nonconforming approximation to $H(\text{gradcurl};\Omega)$ and $[H^1(\Omega)]^3$, can form a discrete Stokes complex together with the Lagrange element and the $L^2$ element.

翻译：我们建议对立方线的两组不兼容元素:一组是美元-text{curl{Delta\text{curl}美元问题,另一组是布林克曼问题。$-text{curl{Delta\text{curl}美元的问题是在立方梅什上的第一个不兼容元素。布林克曼问题的元素可以产生一个与参数$(nu$)有关的统一稳定的有限元素方法。美元-text{crl{Delta\text{curl}美元和布林克曼问题的最低级元素分别有48和30度的自由度。元素的两个组合是$H(\text{cur};\奥米加美元和$(text{div};\奥米加)和$H(text{drqurl};\奥米加$(Omega) $和 $($) $($) 和 $($) 美元) 的离心元素组合。