Mixed Jacobi-spherical harmonic spectral method for Navier–Stokes equations

Mixed Jacobi-spherical harmonic spectral method is proposed for the Navier–Stokes equations in a ball. Its stability and convergence are proved. Numerical results demonstrate the efficiency of this approach. Some results on the mixed Jacobi-spherical harmonic approximation are established, which play important role in numerical analysis of spectral method in spherical geometry.