In this paper we propose a stabilized conforming finite
volume element method for the Stokes equations. On
stating the convergence of the method, optimal a priori
error estimates in different norms are obtained by
establishing the adequate connection between the finite
volume and stabilized finite element formulations. A
superconvergence result is also derived by using a
postprocessing projection method. In particular, the
stabilization of the continuous lowest equal order pair
finite volume element discretization is achieved by
enriching the velocity space with local functions that do
not necessarily vanish on the element boundaries.
Finally, some numerical experiments that confirm the
predicted behavior of the method are provided.