I've just checked in the discontinuous Lagrange basis (L2_LAGRANGE) we 
discussed recently. Changing MONOMIAL to L2_LAGRANGE in 
miscellaneous_ex5 works fine in both 2D and 3D.

A few comments:

1. Just like in fe_monomial.C, I set compute_constraints to be a NOOP. I 
was surprised to see that this method is not a NOOP in L2_HIERARCHIC?

2. Similarly, I was surprised to see that L2_HIERARCHIC returns C_ZERO 
rather than DISCONTINUOUS in get_continuity()?

3. In fe_monomial.C, it looks like monomial_n_dofs() and 
monomial_n_dofs_per_elem() are identical? If so, I'd like to delete the 
latter (we only have one of these two functions in L2_HIERARCHIC and 
L2_LAGRANGE)

4. For now I've just used the same "max_order" for L2_LAGRANGE and 
LAGRANGE, since I wanted to do an initial check-in based directly on 
LAGRANGE. But L2_LAGRANGE's Order is no longer related to "element 
order" (e.g. a SECOND on a TRI3 is perfectly fine for L2_LAGRANGE), so 
those extra valid combinations could be added to L2_LAGRANGE... this 
would also have implications for the serendipity shapes functions: we 
currently assume that QUAD8 or HEX20 implies serendipity, but this need 
not be true with L2_LAGRANGE.

5. I followed the L2_HIERARCHIC approach of adding new files 
fe_l2_lagrange_shape_*D.C which are copies of fe_lagrange_shape_*D.C 
with LAGRANGE replaced by L2_LAGRANGE. But it would be possible to just 
call LAGRANGE's shape functions directly, rather than copying and 
pasting --- though this would need some modifications if point 4 above 
is implemented. Any thoughts on the best thing to do here?

Dave


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