I've coded up a Stokes Flow problem using finite elements and am in the process of verifying that it works. I'm just not sure what convergence rate I should be expecting as I globally refine the mesh.

I know for scalar problems using linear basis functions I'd expect order $h^2$ convergence ($h$ is element size), and using quadratic basis functions I'd expect order $h^3$ convergence in the $L^2$ norm and one power less in the $H^1$ seminorm. The problem I'm having now is that when coding Stokes flow I used the Taylor-Hood element which uses linears for the pressure and quadratic for the velocity components. Is it as simple as the velocities converging at $h^3$ and the pressure at order $h^2$?