Numerical verification of stationary solutions for Navier–Stokes problems

We present a numerical method to enclose stationary solutions of the Navier–Stokes equations, especially 2-D driven cavity problem with regularized boundary condition. Our method is based on the infinite dimensional Newton's method by estimating the inverse of the corresponding linearized operator. The method can be applied to the case for high Reynolds numbers and we show some numerical examples which confirm us the actual effectiveness.