For a 2D HDG code, I would like to be able to visualize the solution on the edge space between elements. Basically, this amounts to plotting the solution on the green nodes below.Is there a standard way using VTK / Paraview to plot these values along all the green line segments (using a colorbar)? 
Viewing HDG FEM edge variables in vtk / paraview
discontinuous galerkin;paraview;vtk
Yes -- in VTK you can output data as lines even if you are in 2d (and in 3d). You can see an example here, as part of the deal.II tutorial program step-51: https://dealii.org/developer/doxygen/deal.II/step_51.html#Results