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

摘要

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 H1 error estimate of the finite volume solution uh, and L2 error estimate for ph, are introduced. Finally, we provide a numerical example to confirm the efficiency of the FVM.