The finite volume method based on stabilized finite element for the stationary Navier–Stokes problem

A finite volume method based on stabilized finite element for the two-dimensional stationary Navier–Stokes equations is investigated in this work. A macroelement condition is introduced for constructing the local stabilized formulation for the problem. We obtain the well-posedness of the FVM based on stabilized finite element for the stationary Navier–Stokes equations. Moreover, for quadrilateral and triangular partition, the optimal H1H1 error estimate of the finite volume solution uhuh and L2L2 error estimate for phph are introduced. Finally, we provide a numerical example to confirm the efficiency of the FVM.