Juan,

I would like to ask what would be the best/fastest way to evaluate 
*fe_v.shape_value 
> (i,x), **fe_v.shape_grad* *(i,x)*, in points that are not quadrature 
> points but that are guaranteed to lie within the curved cell/quad.
>
If I understand the situation correctly, you have a FEValues object that is 
initialized on a cell and now you want to evaluate it at an additional 
point that is not included in the mapped quadrature points.
Is that the case? If so, I would either add that point to the existing 
FEValues object or build a separate one that includes the quadrature point 
(with respect to the unit cell) you want to evaluate the shape functions at.
It is sufficient to initialize this separate object for cells for which you 
actually need it.
Maybe, I misunderstand what you want. Can you specify the issue you are 
trying to solve?

Best,
Daniel

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