20 node quadratic hexahedral element

[kinnala]

This begins the work on #327 .

Edit: Includes also a feature for merging two meshes via __add__.

[kinnala]

The convergence rate seems to be lower than I expect; I'm not sure what causes this. Need to investigate a bit further. Most likely an error in the implementation.

[kinnala]

Added several new tests but couldn't find the culprit: still the new element converges as O(h^1/2) in H^1 norm and O(h) in L^2 norm which isn't O(h^2) and O(h^3) as I'd expect.

[kinnala]

Figured out that there could still be a hidden bug in the facet->edge expansion. Added a test in the latest commit.

[kinnala]

Yes! Figured it out. The facet->edge expansion that was fixed in #83 was working only in case of tetrahedral elements.

[kinnala]

Now we have the first quadratic hexahedral element. Do we still need the 27 node element? Maybe for Stokes?

[gdmcbain]

Do we still need the 27 node element? Maybe for Stokes?

Well we probably want it for completeness anyway and yes for Stokes, I think. ElementHex2 is often recommended for Stokes (e.g. Ern & Guermond 2004, Theory and Practice of Finite Elements, figure. 4.4), but I don't think I've seen serendipity elements used for incompressible fluids.

[kinnala]

Well we probably want it for completeness anyway and yes for Stokes, I think.

Sure. That can be my next follow up task.