>
> OK, so F_i would then be (f(u),\varphi_i), right? 
>
> I think the question is whether you do or do not apply 
> ConstraintMatrix::condense to F. I never really know whether you do or 
> do not have to do that when you want to use F that way, so I typically 
> just assemble the (scalar number) 
>    (f(u),v) 
> directly. 
>

Hi Wolfgang, a brief update -- before, I was using 
ConstraintMatrix::distribute_local_to_global in the assembly of both the 
derivative vector and the Hessian matrix. I can see how that would make the 
computed vector no longer represent the derivative of a functional, since 
you're changing entries more to make the hanging node constraints come out 
correctly. To see if this was the issue, I instead changed the code to add 
up contributions to the global vector/matrix directly, and only reconcile 
the constraints in the nonlinear solver routine. All the other unit tests 
still pass, so this change didn't break the nonlinear solver for the 
unrefined case. Still, the errors in the local linear approximation to P 
aren't decreasing for the refined mesh.

I'll try your approach about assembling (f(u), v) directly and report back. 
If you have other suggestions, I'm all ears; this is a pretty serious 
roadblock for what I want to do next.

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