Hi James, cc everyone, In response to your question on slack earlier, it depends a little what you want. If you want spectral elements, as in high order finite elements, then the element tabulator FIAT supports them for intervals now, though they need some plumbing into UFL since there don't seem to be the right aliases set up at that level.
From that you can get high order elements on quadrilaterals using the tensor element functionality, although you won't get very good performance in assembly because we don't yet support the sum factorisation algorithm which is required to do that. Miklos is currently working on making that go.
If you want triangles then life is somewhat more complicated and you'd need to do significantly more work in FIAT. We could talk about that. If you actually want to make a spectral model (i.e. one mega-high order element) then Firedrake may well not be the right tool, and we should talk about what you really need. Regards, David