Mixed order recovery

[Witt-D]

Code to build/find the necessary spaces for recovered transport for lowest order / mixed order finite element domains.

Spaces are found and build bespoke to the family of the de-Rham complex

[jshipton]

Great - thanks @Witt-D ! We need a / some tests(s) for this - I can't see that the new code is currently used anywhere...

[tommbendall]

Great - thanks @Witt-D ! We need a / some tests(s) for this - I can't see that the new code is currently used anywhere...

I think we could use this in some existing tests:

• the dry Bryan and Fritsch example (https://github.com/firedrakeproject/gusto/blob/main/examples/compressible/dry_bryan_fritsch.py)
• the unsaturated bubble example (https://github.com/firedrakeproject/gusto/blob/main/examples/compressible/unsaturated_bubble.py)

And if we want to be really thorough, we should add a unit-test specifically testing that the spaces set up have the appropriate degrees

[jshipton]

@tommbendall do we need an integration test or example that sets up and runs a problem on mixed order spaces?

[tommbendall]

@tommbendall do we need an integration test or example that sets up and runs a problem on mixed order spaces?

We could add a travelling vortex to the examples? But I think that could also happen in a different PR