Convergence of a Finite Volume Schemes for the Incompressible Navier-Stokes Equations

Abstract The topic of this work is the discretization of stationary incompressible Navier-Stokes equations in two dimensions by the cell centered finite volume method. The main results of this work are the existence and the uniqueness of the finite volume discrete problem and the convergence of the velocity in the L2 norm and the discrete norm. Our techniques are based on the construction of a space discretization, a new variational formulation, the compactness theorem and the discrete Poincaré inequality.