A quadrilateral, anisotropic, superconvergent, nonconforming double set parameter element

In this paper, a four-parameter quadrilateral nonconforming finite element with double set parameter (DSP) is presented. The element is originated from the nonconforming rotated Q1 element and bilinear element, thus we can call it QB element. We prove that it is an anisotropic and superconvergent nonconforming quadrilateral finite element. The results of this paper can be regarded as extensions of the DSP method to the second order problems, which show some new merits of it. Finally, numerical results are presented, which coincides with our theoretical analysis.