>
> For a rectangular bilinear lagrange element we define two parameters "a" 
> and "b". They define the width b and height a of the rectangle within 
> physical coordinates. The Jacobian matrix, B-operator, stiffness matrix 
> etc. can all be computed then using this special case formulas. 1 and 1 
> means a = b = 1, so we obtain a square with same width and height in an 
> amount of 1.
>
> I expect the Jacobian matrix to be 
>
>     b/2     0
>      0      a/2
>
> For the previous cube where I used a=b=2, hence a square with width and 
> length 2, we should receive the following:
>
>      1     0
>      0     1
>
> But if you compare this to my results above, I receive 2 instead of 1? Why?
>
The reference cell [1] we are using is [0,1]^d and not [-1,1]^d. Therefore, 
your result differs by a factor 2.


> Limited means, if you try to access data from a vector/matrix, either you 
> receive an error or just 0 since the matrix has only values where you store 
> them. In this case I can just put 10 as first index, it still gives me 
> values, e.g. -3.9853 something.
> This makes no sense to me. For shape functions I checked. Only values from 
> n_q_points x dofs_per_cell are stored there, rest is 0. But here it seems 
> different. Or am I overseeing something?
>
fe_values.get_jacobians (); is a std::vector so we actually don't control 
access to the elements directly from deal.II. If you are trying to access 
memory out of range you might not get an error as operator[] does not throw 
exceptions.
You can use std::vector::at() for checking that the index is inside the 
bounds of valid elements in the std::vector.

Best,
Daniel

[1] 
https://www.dealii.org/8.4.1/doxygen/deal.II/DEALGlossary.html#GlossReferenceCell


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