A new superconvergence property of nonconforming rotated Q1 element in 3D

Nonconforming rotated Q1 finite element method is used to approximate the general second-order elliptic problem in 3D. A new superconvergence property at eight vertices and six face centers of each element is proved. Several cheap numerical integration schemes are proposed for solving the discrete problem, which include schemes with only two nodes. All schemes yield optimal H1, L2 error bounds as well as the superconvergence property. Extensive numerical results are presented to confirm the theoretic prediction.