A cheapest nonconforming rectangular finite element for the stationary Stokes problem
We introduce a least degrees of freedom nonconforming finite element pair to approximate the Stokes equations based on quadrilateral meshes. The finite element space for the velocity field is composed of the P1 P 1 -nonconforming quadrilateral element plus only one additional global DSSY (DouglasSantosSheenYe) or RT (RannacherTurek) type of bubble function. The pressure field is approximated by the piecewise constant function. We show that the discrete problem is nonsingular and the element pair satisfies a weak discrete infsup condition. Several numerical examples are shown to confirm the efficiency and reliability of the proposed method.
nonconforming finite element stokes equations bubble function