Macro Stokes Elements on Quadrilaterals

Abstract

We construct a pair of conforming and inf–sup stable finite element spaces for the two–dimensional Stokes problem yielding divergence–free approximations on general convex quadrilateral partitions. The velocity and pressure spaces consist of piecewise quadratic and piecewise constant polynomials, respectively. We show that the discrete velocity and a locally post–processed pressure solution are second–order convergent.