The control operator doesn't accumulate in the residual. Instead the
localoperator has a member vector where the value of the derivative is
accumulated.

In that case you need two GridFunctions, which can be
bound to the two cells.

After consulting Steffen

It makes the code generation workflow more complicated without
contributing anything substantial

Instationary stuff not fixed so far.

The previous name was *really* confusing.

Much more telling name...

Useful, if you are only interested in the jacobian_apply versions
anyway.