Hey Kyunghoon,
                          If you are using FEMSystem, then adjoints ex_1
has examples of evaluating Quantities of Interest (QoIs) of the kind you
are describing. Essentially, we overload the postprocess,
element_postprocess and side_postprocess functions to do the particular
post processing we want to do.

Overloading element_postprocess will allow you to compute \in_{\Omega} u
d\Omega and side_postprocess will allow you to compute \in_{\Gamma} u
d\Gamma

Thanks.

On Tue, Feb 5, 2013 at 10:20 PM, Kyunghoon Lee
<[email protected]>wrote:

> Dear all,
>
> I'd like to evaluate outputs after solving the 2D Poisson example; for
> instance, the sum of u over the entire domain, \in_{\Omega} u d\Omega, and
> the sum of u over specific boundaries, \in_{\Gamma} u d\Gamma.  I guess I
> need to put some codes for output evaluations after
>
> equation_systems.get_system("Poisson").solve();
>
> , but I'm not sure of what to do --- do I need to create some assembly
> functions for output evaluations then attach to the system?  I'd appreciate
> it if someone could show necessary steps briefly.
>
> Best regards,
> K. Lee.
>
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> Vikram Garg
> Postdoctoral Associate
> Center for Computational Engineering
> Massachusetts Institute of Technology
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