Abstract: In this paper, we discuss a stabilized fractional-step method for numerical solutions of the time-dependent Navier-Stokes equations. The nonlinear term and incompressible condition are separated into two different sub-problems by virtue of the operator splitting method, where the nonlinear term is treated by Oseen iteration. The linear elliptic problem is solved at the first step, and the second step is to solve the generalized Stokes problem. The two problems both satisfy the homogeneous Dirichlet boundary conditions for the velocity. Furthermore, a locally stability term is added in the second step of the scheme, which enhances the numerical stability and efficiency for the equal-order pairs. The convergence analysis and error estimates for the velocity and pressure of the schemes are established via the energy method. Some num-erical results demonstrate the efficiency of the proposed method.

Key words: projection methods, stabilized finite element method, Navier-Stokes equations, error estimates