I think there must be some correspondence between dofs and locations,
but I can't work out how to extract it. I was going to use support
points, but I am dealing with discontinuous elements so the cells don't
have any.

DoFTools::map_dofs_to_support_points is what you're looking for :-)

Cheers
 W.

------------------------------------------------------------------------
Wolfgang Bangerth               email:            [email protected]
                                www: http://www.math.tamu.edu/~bangerth/

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