TY - JOUR T1 - Constrained Quadrilateral Nonconforming Rotated $Q_1$ Element AU - Jun Hu & Zhong-Ci Shi JO - Journal of Computational Mathematics VL - 6 SP - 561 EP - 586 PY - 2005 DA - 2005/12 SN - 23 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8839.html KW - Constrained, Nonconforming Rotated $Q_1$ element, Superconvergence, Postprocess. AB -

In this paper, we define a new nonconforming quadrilateral finite element based on the nonconforming rotated $Q$1 element by enforcing a constraint on each element, which has only three degrees of freedom. We investigate the consistency, approximation, superclose property, discrete Green's function and superconvergence of this element. Moreover, we propose a new postprocessing technique and apply it to this element. It is proved that the postprocessed discrete solution is superconvergent under a mild assumption on the mesh.