You can't. There is no obvious relationship between the two for
*generalized* support points. There may be more, or fewer generalized
support points than DoFs on a cell.
Of course there is no obvious relationship but I would assume that
there is some relationship between them (not necessarily unique in any
direction). I guess you are saying is that we are currently not
exposing any relationship between them.
It's all essentially internal to the FE classes. The FE class exports
where it likes stuff to be evaluated (these are the generalized support
points) but how it uses the resulting vector of values to obtain DoF
values is up to the internals of the FE class again. The two places (the
description of where the generalized support points are, and the place
that converts function values at generalized support points to DoF
values) just need to agree on the order of points. But because both of
these are in the same class, they may choose any perturbation of points.
A FE may also describe more support point that it then decides to not
use. There really is not required relationship between the two.
In other words, it's up to every FE to decide what it wants things to
be. Some FEs may have more generalized support points than DoFs, others
less.
The reason I am asking is that I would like to differentiate between a
generalized support point in the interior of the cell that just
happens to be on a face and a face dof (for example FE_DGQ vs FE_Q).
This question does not make sense. If you have a modal (as opposed to
nodal) element, then *all* generalized support points will be used in
determining *each* modal DoF value. You cannot say that some generalized
support points are associated with specific DoFs.
get_associated_geometry_primitive answers this for DoFs, but it looks
like I am out of luck tying this back to support point locations
unless I have n_dofs_per_cell unit_support_points and no
generalized_support_points. So I can do this for FE_DGQ but not for
Nedelec or other elements. Does that sound about right? I was hoping
there is an easy way to query this information.
Yes, this is correct. No easy way -- in fact: no way, period -- because
there is no relationship.
3. Elements like FE_QLegendre return 0 generalized support points. Is
there any information I can extract from the FE about the degrees of
freedom or support points in this case?
I should say that the fact that FE_QLegendre doesn't publish GSPs is
functionality that is missing, not because it can't define them. It's
just that nobody has implemented this so far.
Best
W>
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Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
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