Thanks. I see things clearer now, hopefully. If everything is defined on a 
unit cell [0,1]^d, how can I output FEValues quantities in the unit cell 
first. From what I understand now, we receive the quantities directly on 
the real cell (reference cell). Hence, using fe_values.reinit(cell) we 
compute only necessary things depending on the similarity of the current 
cell to the unit cell. Am I still able to check the quantities on the unit 
cell somehow and than map them to the real cell, or at least output both to 
understand more clearly how things work?

I checked the unit cell coordinates by means of 
GeometryInfo<dim>::unit_cell_vertex() and receive the following:

UNIT CELL COORDINATES

0   0   
1   0   
0   1   
1   1

But as already mentioned I still have unmapped quantities such as:


GAUSS POINT COORDINATES

-0.57735   -0.57735   
0.57735   -0.57735   
-0.57735   0.57735   
0.57735   0.57735

>From what I understood the shape functions will not change for a standard 
FE_Q element, if it is not a Raviart-Thomas element. But shape function 
gradients, jacobians, GAUSS points, etc. will change.

Is it possible now to output unit cell shape function gradients or 
quadrature points before they are mapped?

Kind regards,
Seyed Ali Mohseni
 

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