Comments on Lagrange elements

[jpdean]

Here are some small issues I've noticed when looking over Lagrange elements:

Alternative names

• [ ] The name "polynomial" doesn't seem very helpful, since many/most finite element bases are polynomials.
• [ ] I'm also not really a fan of DGT (which I think stands for Discontinuous Galerkin Trace). I don't think it makes much sense, but since it's used in UFL we should probably keep it.
• [ ] DGT and Q should probably be moved to the "Abbreviated names" section.
• [ ] The variants are listed in "Alternative names". Is this what we want?

De Rham complex families

• [ ] The pyramid and prism elements are missing from here. For example, $[S_{1, k}^{\mathrm{prism}}]_d$ is a (discontinuous) Lagrange element (see Cockburn and Fu 2017)

Abbreviated names

• [ ] I've never really liked "CG" and "DG" as element names, but, again, since they're in UFL we should probably keep them!

Degrees

• [ ] Currently says $1 \leq k$, which is true for continuous Lagrange elements and is, of course, required for $H^1$-conformity. However, we also include the discontinuous Lagrange spaces on this page (e.g. "DG" and $\mathcal{P}_k \Lambda^d$), which are defined for $k = 0$. I guess it depends on if we are talking about the elements themselves or the finite element space they construct

Polynomial superdegree

• [ ] Maybe I missed it, but I couldn't find some of these in the references given. The results for quads and hexes are given in e.g. "Theory and practice of finite elements" by Ern and Guermond. We should probably add references for prisms and pyramids too if I haven't just missed them

Polynomial set

• [ ] Again, I couldn't find $\mathcal{Z}_k^{(15)}$ or $\mathcal{Z}_k^{(16)}$ defined in the references on the page

Number of DOFs / DOFS on sub-entities

• [ ] Again, maybe we need some extra references for prisms and pyramids, or maybe I just missed it

Continuity

• [ ] This says "function values are continuous", but again, we have discontinuous Lagrange elements on this page.

If you agree with any of these, let me know and I'll make a PR to address them!