> The derivatives with respect to the 
> mesh points will be needed for optimization purposes.

I’m not familiar with the algorithms used in shape optimisation, but one 
*possible* work-around if you need derivatives wrt. the mesh points on the 
finite element cell level would be to do the following:
- Add an extra component to an FESystem, specifically a FE_Q(1)^dim. You would 
interpret as the current position of the mesh vertices because the support 
points for this FE coincide with the grid vertices.
- You can initialise this field using VectorTools::interpolate. Specifically 
you would simply populate the relevant entries of the result returned by this 
Function with the coordinates given by the input Point<dim>.
- Now that you have these “extra DoFs”, you can now compute the sensitivities 
on any cell with respect to them.

This, of course, would not really help if you compute some objective function 
based on the entire solution, and you in fact need your entire program to de 
differentiable.

Best,
Jean-Paul

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