For the Crouzeix-Raviart and enriched Crouzeix-Raviart elements, asymptotic expansions of eigenvalues of the Stokes operator are derived by establishing two pseudostress interpolations, which admit a full one-order supercloseness with respect to the numerical velocity and the pressure, respectively. The design of these interpolations overcomes the difficulty caused by the lack of supercloseness of the canonical interpolations for the two nonconforming elements, and leads to an intrinsic and concise asymptotic analysis of numerical eigenvalues, which proves an optimal superconvergence of eigenvalues by the extrapolation algorithm. Meanwhile, an optimal superconvergence of postprocessed approximations for the Stokes equation is proved by use of this supercloseness. Finally, numerical experiments are tested to verify the theoretical results.

翻译：针对Crouzeix-Raviart和富化Crouzeix-Raviart单元，通过建立两种伪应力插值，推导了Stokes算子特征值的渐近展开式，这两种插值分别关于数值速度和压力实现了满一阶超逼近。这些插值的构造克服了两种非协调单元因标准插值缺乏超逼近性带来的困难，并引出了数值特征值内在且简洁的渐近分析，从而通过外推算法证明了特征值的最优超收敛性。同时，利用该超逼近性，证明了Stokes方程后处理近似解的最优超收敛性。最后，通过数值实验验证了理论结果。