A Weak Galerkin Finite Element Method for the Navier-Stokes Equations

In this paper, a weak Galerkin finite element method (WGFEM) is proposed for solving the Navier-Stokes equations (NSEs). The existence and uniqueness of the WGFEM solution of NSEs are established. The WGFEM provides very accurate numerical approximations for both the velocity field and pressure field, even with very high Reynolds numbers. The salient feature is that the flexibility of the WGFEM for the choice of the order of the velocity and pressure comparing to the standard finite element methods. Optimal order error estimates in both vertical bar.vertical bar W-h and L-2 norms are proved for the semi-discretized scheme. Numerical simulations are presented to show the efficiency of the WGFEM.