Samuel,

I am attempting to implement a hp hybridized dg-method for solving 
> ellipctic problems in deal.II. I am relying on steps 27 and 51 of the 
> deal.II tutorial programs. However, when I try to group some FE_FaceQ 
> elements in an hp::FeCollection and distribute the degrees of freedom, I 
> get an ExcNotImplemented() exception thrown by some method 
> hp_vertex_dof_identities. Am I getting something wrong? Or is this feature 
> just not implemented for
> FaceQ yet?
>
This feature is just not implemented yet. As FE_FaceQ is in fact 
discontinuous, you can try to just copy
hp_vertex_dof_identities, hp_line_dof_identities and hp_quad_dof_identities 
from source/fe/fe_dgq.cc to source/fe/fe_faceq.cc.
If you are successful with this, we would gladly accept a patch.  :-)

Best,
Daniel

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