Turning FEniCS functions into structured field

I would suggest using VTKplotter (see; New vtkplotter module for visualization) or Paraview for 3D visualization.
Note that you can plot 2D fields with matplotlib using built in dolfin functions, see for instance: https://bitbucket.org/fenics-project/dolfin/src/master/python/demo/documented/stokes-taylor-hood/demo_stokes-taylor-hood.py

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