  The goal of this paper is to introduce a simple finite element method to
solve the Stokes and the Navier-Stokes equations. This method is in primal
velocity-pressure formulation and is so simple such that both velocity and
pressure are approximated by piecewise constant functions. Implementation
issues as well as error analysis are investigated. A basis for a divergence
free subspace of the velocity field is constructed so that the original saddle
point problem can be reduced to a symmetric and positive definite system with
much fewer unknowns. The numerical experiments indicate that the method is
accurate and robust.
