A defect-correction method based on equal-order finite elements for the incompressible flows (I)

A defect-correction method based on equal-order finite elements for the incompressible flows with a high Reynolds number is considered. This new finite element method satisfied inf-sup stability and enjoys tow prominent features: stabilization of convection-dominated flows, and decrease of computation time by constructing a linear residual correction algorithm in each correction step. Continuous equal-order finite elements for both velocities and pressures, and a backward Euler method for the time approximation are used. The stability and convergence of the velocities are proved. The error estimation results show that one-step correction improves first-order spatial accuracy of velocities regardless of the Reynolds number.