Superconvergence of some nonconforming brick elements for the 3D Stokes problem

In this work, we study the superconvergence of three nonconforming brick elements for the 3D Stokes problem: a nonconforming rotated Q1 type element, the reduced version of this element and an edge-face-based element. The superclose interpolations are different from the canonical ones, and superclose analyses for the consistency error are also given, ensuring an O(h2)-order for both the velocity and the pressure for all these elements. By applying suitable postprocessing techniques, global superconvergence can be derived. Numerical examples are presented to confirm our theory.