Yeah, thats pretty much it. Judging from the output, each of your 
FEExtractors is vector valued, so fe_values[N_density] returns a 
vector-valued view and fe_values[N_density].value(i, q_point) is the i'th 
vector valued *shape function* (not DoF value) associated for the N_density 
field at the i, q_point quadrature point. It is indeed not connected to the 
solution vector. But value() is just one of the functions that FEValuesViews 
- do any of the other functions appear more helpful in terms of what you're 
trying to achieve?

On Saturday, August 5, 2017 at 2:27:49 PM UTC+2, Maxi Miller wrote:
> I think I understand my problem (slowly):
> Using the project-function means that I write the initial conditions into 
> my solution-vector. But when I call fe_values[N_density] I get a view on 
> the finite element-variable, which is not connected to the solution-vector. 
> Thus I get (in the last line) the value of the i-th degree of freedom at 
> the q-point-th point in the grid. Now, when iterating over the degrees of 
> freedom, the first degree of freedom will be in x-direction (if looking in 
> a cartesian coordinate system), the next one in y-direction and the last in 
> z-direction, thus being the base vectors for a 3d grid, but they are not 
> connected to the values set before in the project-function. Is that 
> correct? Or did I still misunderstand something?

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