A mixed stream-function and vorticity formulation for axisymmetric Navier–Stokes equations

We present a mixed formulation of the axisymmetric steady-state incompressible Navier–Stokes equations. The new unknowns are the stream function and the vorticity. Spectral methods are used to approximate the continuous problem. We prove that the error estimates between the exact and the discrete solutions are optimal. We use the Glowinski–Pironneau algorithm for the implementation of the discrete problem and give numerical results.