A stabilized finite volume method for the stationary Navier–Stokes equations

In the present paper, we propose a stabilized finite volume element method for the Navier–Stokes equations using the lowest order P1−P0P1−P0 element pair. The stabilized method is designed by adding a jump term of the discrete pressure to the continuity approximation equation. A discrete inf–sup condition is established for the stabilized finite volume element scheme which assures the stability of the discrete solutions. The optimal error estimates are derived in the H1-norm for velocity and the L2-norm for pressure, respectively. Moreover, the optimal L2- error estimate is also given for velocity approximation.