[firedrake] Pass approximate Jacobian to derivative() call

[Buesing, Henrik]

> > is it possible to just pass the approximate Jacobian to the derivative
> > call? Since it's so complicated in my case to get the exact Jacobian I
> > would like to do sth. like
> >
> >
> >
> > du = [(F(u + h) - F(u - h))/(2*h)]
> 
> So you can't do this by passing something to derivative (which instead
> computes the jacobian for you given a residual). 


 [Buesing, Henrik] Yes, true. I mixed this up. I want to do 

solve(F == 0, u, J=approximate symbolic Jacobian)

> 
> You can instead of course build an approximate, symbolic, Jacobian "by
> hand" and provide that to the solver: you'll then end up doing quasi-
> newton, rather than newton.

[Buesing, Henrik] That's what I would like to do. In my multi-physics case (see attachement) the Jacobian would have a 2x2 block structure. 

I'm unsure how to provide this... I tried to write sth. down for the blocks (see test.py), but this is obviously wrong.

Thank you for your help!

Henrik



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