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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 $h^2$?

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  • $\begingroup$ This question is gathering some close votes (though none from me). It may find a better reception at scicomp.stackexchange.com $\endgroup$
    – j.c.
    Jul 15, 2014 at 15:56
  • $\begingroup$ I don't understand why it would be closed here, but I will try at the scicomp stackexchange. Thanks. $\endgroup$
    – Lukas Bystricky
    Jul 16, 2014 at 16:13
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    $\begingroup$ 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.) $\endgroup$
    – Christian Clason
    Jul 16, 2014 at 17:49
  • $\begingroup$ It looks like SciComp has answered this satisfactorily. $\endgroup$
    – S. Carnahan ♦
    Jul 18, 2014 at 23:06

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