A spectral approximation scheme for the Stokes equations

The two-dimensional steady state Stokes equations are considered. By introducingthe vorticity to the stream function form of the Stokes equations, we have a coupled system of two elliptic equations. An efficient approximation scheme for solving the equations is introduced. The method consists of finding the trace of the normal derivative of the vorticity by means of the trace and the inverse Green operators. This method is noniterative in the sense that the vorticity is obtained directly from the trace of its normal derivative. Convergence of our scheme is proved and numerical experiments are presented.