A Weak Galerkin Finite Element Method for the Navier-Stokes Equations (Communications in Computational Physics, 2018)
In this paper, a weak Galerkin finite element method (WGFEM) is proposedfor solving the Navier-Stokes equations (NSEs). The existence and uniqueness of theWGFEM solution of NSEs are established. The WGFEM provides very accurate numericalapproximations for both the velocity field and pressure field, even with veryhigh Reynolds numbers. The salient feature is that the flexibility of the WGFEM forthe choice of the order of the velocity and pressure comparing to the standard finite elementmethods. Optimal order error estimates in both |·|$W_h$ and $L^2$ norms are provedfor the semi-discretized scheme. Numerical simulations are presented to show theefficiency of the WGFEM.