Add real element to DOLFINx

[jorgensd]

Add the notion of real element to DOLFINx. Implemented based on https://github.com/scientificcomputing/scifem/blob/main/src/scifem.cpp
Relies on FEniCS/basix#1001

One should not be able to make a mixed_element with real element. One should use the block constructor (i.e. MixedFunctionSpace or manually block it).

The real element is now:

• A DG-0 element in basix, gives the exact same kernel as with a DG-0/Constant.
• Gives the ownership of the DOF to the first process that has a cell (sometimes rank 0 has no cell).

[jorgensd]

Resolves: #225

[michalhabera]

One should not be able to make a mixed_element with real element. One should use the block constructor (i.e. MixedFunctionSpace or manually block it).

You mean that you cannot create a Real element with nontrivial shape, but should work in MFS?

[jorgensd]

One should not be able to make a mixed_element with real element. One should use the block constructor (i.e. MixedFunctionSpace or manually block it).

You mean that you cannot create a Real element with nontrivial shape, but should work in MFS?

No, one should not be able to do:

el = basix.ufl.element("Lagrange", mesh.basix_cell(), 2)
r_el = basix.ufl.real_element(mesh.basix_cell(), shape=(2,))
me = basix.ufl.mixed_element([el, r_el])

but one can do:

el = basix.ufl.element("Lagrange", mesh.basix_cell(), 2)
V = dolfinx.fem.functionspace(mesh, el)
r_el = basix.ufl.real_element(mesh.basix_cell(), shape=(2,))
R = dolfinx.fem.functionspace(mesh, r_el)
W = ufl.MixedFunctionSpace(V, R)
u, lmbd = ufl.TrialFunctions(W)
v, mu = ufl.TestFunctions(W)

[michalhabera]

This change is minimal and nicely isolated. I like you've added custom dofmap builder and did not try to tweak the existing one -- which was the bad design in legacy FEniCS if I remember well.

I still believe we should follow matrix-free/MATSHELL approach for all these extremely skew spaces, but this is a good solution until we have more time to work on the alternative.

[jorgensd]

This change is minimal and nicely isolated. I like you've added custom dofmap builder and did not try to tweak the existing one -- which was the bad design in legacy FEniCS if I remember well.

I still believe we should follow matrix-free/MATSHELL approach for all these extremely skew spaces, but this is a good solution until we have more time to work on the alternative.

In combination with:
#3938
we should be able to use matrix free approach with this element with no changes to the core.

[jhale]

Can use auto, type explicit in use of make_shared

[jorgensd]

But we are not using a make_shared pointer here as it is not used further down the line?