Abstract
Two quadrilateral low-order equal-order finite element schemes are analyzed for Stokes equations. Both of these schemes adopt the quadrilateral P1-nonconforming finite element to approximate the pressure over a coarser mesh. The velocity spaces are constructed over a finer mesh, where the standard Q1-conforming element space and the quadrilateral P1-nonconforming element space are selected, respectively. The stability assertion is given for each pair. Moreover, the superconvergence property of the pressure is obtained over uniform rectangular meshes. All the analyses above are verified by numerical tests.
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