A Finite Volume Method Based on the Constrained Nonconforming Rotated Q1-Constant Element for the Stokes Problem

We construct a finite volume element method based on the constrainednonconforming rotated Q₁-constant element (CNRQ₁-P₀) for the Stokes problem.Two meshes are needed, which are the primal mesh and the dual mesh. We approximatethe velocity by CNRQ₁ elements and the pressure by piecewise constants.The errors for the velocity in the H¹ norm and for the pressure in the L² norm areO(h) and the error for the velocity in the L² norm is O(h²). Numerical experimentsare presented to support our theoretical results.