Real element

[jorgensd]

From a basix point of view, a real-element is a DG-0 element. It is only DOLFINx that needs to know about this at dofmap construction ref (https://scientificcomputing.github.io/scifem/examples/real_function_space.html, https://github.com/scientificcomputing/scifem/blob/main/src/scifem.cpp#L60-L109)
Therefore, I don't see why we have https://github.com/search?q=repo%3AFEniCS%2Fbasix%20real_element&type=code
which I believe is untested and doesn't work with DOLFINx.

If it works it would be good to add a demo to DOLFINx with it.
If not, I think we should create a different kind of wrapper in basix to instruct DOLFINx to use a dofmap constructor similar to the one in scifem.

[mscroggs]

I'm fairly certain that the Basix Real element doesn't work. I'll open a PR to remove it

[jorgensd]

I had a discussion with @michalhabera about real elements today, and I guess one thing that makes the "real" element differ from a DG-0 element, is that the dof shouldn't really be associated with the cell, as it is shared across all faces.

For more complex, "global" elements this would not be so easy to encode with the existing elements.