A pp-version two level spline method for 2D Navier–Stokes equations

We propose a pp-version two level method for the spline solutions of the Navier–Stokes equations in stream function formulation. The new two level method can significantly accelerate the corresponding one level method, especially when the degrees of the spline spaces are greater than 5 in two dimensional case. The convergence analysis as well as the error estimation is given, which is asymptotic optimal with respect to the degrees of the spline spaces. Several numerical examples are presented to validate the theoretical analysis and show the efficiency of the proposed two level spline method.