Hi Michael,
I think you should have a look at FE_Q (Lagrange elements) at this link 
<https://www.dealii.org/current/doxygen/deal.II/classFE__Q.html>. In 
deal.II, the reference cell's domain is [0,1]^2 for 2d element. So, the 
point you are about to evaluate (to get the value of phi_i equal 0.25)  is 
(0.5, 0.5).
You can refer to this snippet:
/*
*  const FE_Q<2> Q_2d_element(1);*
*  const Point<2> center(0.5, 0.5);*
*  for(int i=0; i<Q_2d_element.n_dofs_per_cell(); i++){*
*    std::cout << Q_2d_element.shape_value(i, center) << std::endl;*
*  }*
*/
//output 0.25 0.25 0.25 0.25
Also  have a look at step-3 
<https://www.dealii.org/current/doxygen/deal.II/step_3.html> to understand 
how FE_Q works in real problem since the shape functions will be evaluated 
at real cell coordinates. Good luck.

Regards,
T.P

Vào lúc 07:48:35 UTC+9 ngày Thứ Bảy, 11 tháng 9, 2021, lian...@gmail.com đã 
viết:

> Deal deal.ii comunity,
>
> I want to require the value of a shape function at some quadrature point. 
> But the following code throws an error saying finite_element_output is 
> protected.
>      
> double shape_value = fe_values.finite_element_output.shape_values(i, q_index);
>
> For a 2D bilinear element, I expect the shape values  at the cell 
> center(kesi=0, eta=0) are 0.25 for all the 4 shape functions.
>               [image: Screenshot 2021-09-10 164654.png]
> Is there other way to acquire this information?
>
> Best,
> Michael
>

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