I have an equation -$u''=1,~~x\in(0,1)$. I solved it numerically by Finite element method. and find an approximate solution. $u_{h}$. As you know to do this I defined bilinear and linear functionals for weak formulation s.t
a(u,v)=l(v) for every v in $H_{0}^{1}$ where
a(u,v)=$\int_{0}^{1}u'v'dx$ and l(v)=$\int_{0}^{1}vdx$.
But to find a functinal estimates, |J($u-u_{h}$ )|, I defined a functinal J(v)=$\int_{0}^{1}vdx$ and try to find z in dual problem a(v,z)=J(v) for every v in $H_{0}^{1}$
and I solved the dual problem then find approximation for z.
But J($u-u_{h}$)=a($u-u_{h}$,z)=a(u,z)-a($u_{h}$,z) =l(z)-a($u_{h}$,z)$~~~~~~~$ (**)
(**) is called the error indicator and my questions is that how can I find it ?