> 1) The first is an anistropic vector Lagrange element Q_{k-1,k,k} X
> Q_{k,k-1,k} X Q_{k,k,k-1}
> where k = 2 and the element is discontinuous in the k-1 direction.
At least in 2d, this is exactly the Nedelec element. (Or, rather: It is
the space spanned by the Nedelec element; the Nedelec element is a
particular choice of node functionals that can be used to represent this
space.)
I think Markus makes an excellent suggestion: don't start with the
finite element or a discrete space, but rather start with a description
of the continuous space. The point is that there really seems to be a
mismatch here: all the elements you propose seem to be suggest that you
are working with the H(curl) space. But you can't impose normal
component boundary conditions on functions in H(curl). That has nothing
to do with the Nedelec or any other element, but everything with the
function space H(curl).
It's not a coincidence that you can't impose normal component conditions
on Nedelec elements: the Nedelec space is a subset of H(curl), and
H(curl) doesn't allow you to impose normal components. If you want to
impose normal components, the proper space is H(div), and the elements
that approximate this space are the Raviart-Thomas elements.
Best
Wolfgang
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