A STABILIZED DEFECT CORRECTION METHODS BASED ON EQUAL-ORDER ELEMENTS FOR THE STATIONARY NAVIER-STOKES EQUATIONS
Navier-Stokes方程的一种等阶稳定化亏量校正有限元法

We consider the synthesis of a recent polynomial pressure projection stabilization method with defect correction methods for the incompressible Navier-Stokes equation with a small viscosity coefficient. The combination combines the best features of each. Firstly, it is stable for the equal-order combination of discrete continuous velocity and pressure spaces. Secondly, in the defect step, the artifical viscosity parameter σ is added to the viscosity coefficient as a stability factor. The existence and uniquence are proved for the each step, error estimation is derived for the each step too. The error estimation results show that each step of defect correction method improves the error in the previous step by one power of h.