Hi, nowadays I'm learning about the goal oriented error estimator and I 
read the tutorial of step-14 (
http://www.dealii.org/developer/doxygen/deal.II/step_14.html.) But I'm 
confused about some problems and hope you can help me with these:
1. When deriving the error with respect to the functional, why must we 
change J(e)=a(e,z) to J(e)=a(e,z-z_h) ?
I know the dual solution z must be approximated in a richer space than the 
primal solution, otherwise J(e) will be 0. But why not just solve the dual 
problem in a richer space without subtracting its interpolation to the 
primal space? I didn't see the necessity to introduce z_h into the formula.
2. Why must we change J(e)=∑(f+△ uh,z-zh)-(∂uh,z-zh) to J(e)=∑(f+△ 
uh,z-zh)-(1/2[∂uh],z-zh)? Is it just an implementation consideration for 
saving computational effort? Can this kind of rewriting be generally 
adopted in other kind of problems(e.g in advection problem where the face 
integrals in J(e) relies on the upstream information)?
Thank you very much!

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