Analysis of a finite volume element method for the Stokes problem

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. The stabilization of the continuous lowest equal order pair finite volume element discretization (P1 − P1) is achieved by enriching the velocity space with bubble-like functions. Finally, some numerical experiments that confirm the predicted behavior of the method are provided.