We construct a finite volume element method based on the constrained
nonconforming rotated Q_{1}-constant element (CNRQ_{1}-P_{0}) for the Stokes problem.
Two meshes are needed, which are the primal mesh and the dual mesh. We approximate
the velocity by CNRQ_{1} elements and the pressure by piecewise constants.
The errors for the velocity in the H^{1} norm and for the pressure in the L^{2} norm are
O(h) and the error for the velocity in the L
2 norm is O(h^{2}). Numerical experiments
are presented to support our theoretical results.