In this article, a new recovery method is designed and analyzed for curl conforming elements on cuboid mesh. The proposed recovery method fully exploits the potential of symmetry to obtain the superconvergence of recovered edge finite element solution in discrete ${\ell }_2$ norm. The idea is to identify a symmetry sub-domain such that a polynomial of the same degree is recovered by local $L_2$ projection, based on which the recovered values follow. Combined with extrapolation and the least square fitting for the linear edge elements and quadratic edge elements, respectively, we obtain global superconvergence for recovered quantities in $L_2$ norm. Numerical experiments are provided to validate our theoretical findings.

在本文中，设计并分析了一种新的恢复方法，用于对长方体网格上的卷曲符合元素进行分析。所提出的恢复方法充分利用对称性的潜力来获得离散状态下恢复的边缘有限元解的超收敛性。${\ell }_2$规范。这个想法是要确定一个对称子域，以便通过局部恢复相同程度的多项式${\mathrm{大号}}_2$投影，恢复后的值基于该投影。分别与线性边缘元素和二次边缘元素的外推法和最小二乘拟合相结合，我们获得了回收量的全局超收敛。${\mathrm{大号}}_2$规范。提供数值实验来验证我们的理论发现。