# Finite element convergence rates for mixed problems [closed]

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 $h^2$?

## closed as off-topic by Will Jagy, Stefan Kohl, Steven Sam, Ryan Budney, S. Carnahan♦Jul 18 '14 at 23:06

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• This question is gathering some close votes (though none from me). It may find a better reception at scicomp.stackexchange.com – j.c. Jul 15 '14 at 15:56
• I don't understand why it would be closed here, but I will try at the scicomp stackexchange. Thanks. – Lukas Bystricky Jul 16 '14 at 16:13
• FYI, it's now been posted on SciComp: scicomp.stackexchange.com/questions/14156 (The usual way of things would have been to flag and ask for migration to avoid double content; not sure how that works for a beta site, though.) – Christian Clason Jul 16 '14 at 17:49
• It looks like SciComp has answered this satisfactorily. – S. Carnahan Jul 18 '14 at 23:06