A New Two-grid Algorithm Based on Newton Iteration for the Stationary Navier–Stokes Equations with Damping

Based on finite element discretization, a new two-grid algorithm based on Newton iteration is proposed to solve the stationary Navier–Stokes equations with nonlinear damping term. The proposed new two-grid algorithm consists of three steps: in the first step, we solve one small nonlinear coarse grid problem, and then, in the second and third steps, we solve two linear fine grid problems based on Newton iteration which have the same stiffness matrices with only different right-hand sides. We analyze stability of the present algorithm and prove rate of convergence of the approximate solutions obtained from the algorithm. Numerical results are given to demonstrate the effectiveness of the present algorithm, showing that our algorithm greatly improves the accuracy of the approximate solutions comparable to that of the usual two-grid algorithm.