I'm revisiting the solver approach in the vertical slice model, to try to incorporate it better into dcore. A vertical slice model is obtained from a 3D model, but you assume that all the fields are independent of y, whilst retaining a fully 3D velocity vector. 

There are two ways to achieve this:

1) Build a mesh that is only one element wide and periodic in the y-direction.

2) Split the velocity space into a part which is tangential to the slice plane (u,w), and a part which is normal to the slice plane (v). In compatible FEM this means making a 2D H(div) space for the tangential part, and a scalar DG space for v. 

So far we have been doing 2) in a way that requires rather specialised code that is different from what we use in 3D, which makes the code very bloated and hard to test.

First of all, is 1) possible in Firedrake? If not, how difficult would it be to make it possible? This would be my preferred solution.

If 1) is out, then I'd like to improve our approach to 2) so that it is less intrusive in our code. I'd really like to make a sum of spaces so that we get a 3D vector with the in plane components coming from an H(div) space and the out-of-plane components coming from a DG space. Then, I could call this whole thing my velocity space and e.g. solve mixed velocity pressure problems using it. Is *this* possible? If not, how difficult would it be to make it possible?

all the best

--cjc
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