Thanks for replying me ! 

I moved to squared domain to avoid other possible error when I imply 
boundary condition, but I still have same manufactured solution e^(-x^2-y^2)
I have to say that I have some changed error curve after moving to new mesh 
domain. 
Which is slightly better, but still unsatisfying results. 

<https://lh3.googleusercontent.com/-UR8qKv0nh0o/WBuw-Lg7gFI/AAAAAAAAA8k/FznfGdlllE8OifxsvLJ_Omudg90D611EgCLcB/s1600/error_squared_domain.jpg>

To see error per cell, I referred step 27, and make estimated error data 
out. 

I used following code lines....



 Vector<float> estimated_error_per_cell (triangulation.n_active_cells());

    

    KellyErrorEstimator<dim>::estimate (dof_handler,

                                        QGauss<dim-1>(3),

                                        typename FunctionMap<dim>::type(),

                                        solution,

                                        estimated_error_per_cell);


In fact, I don't know how kelly error estimator works...
but just checked that it usually works well with Poisson Equations.

<https://lh3.googleusercontent.com/-JVGEEcGSQ6E/WBuwfOpt-xI/AAAAAAAAA8g/b8Wjo_cqspAgpz0HEViKz7y6jCz_5ggJQCLcB/s1600/Solution%2Band%2BError%2BEstimator.jpg>

Seeing pictures above,,, when p=2 solution looks seemingly good, but 
estimated error_per_cell should be wrong. 
Since, exact solution the closer points to x=(0,0) (or left down corner in 
pic) has  sharp gradient, thus the larger error is expected. 
Think estimated error case for p=1 is correct. 

Now, I confirmed that the code is not working at higher degree. (p>=2)...
but it is not because of boundary condition...since I have four boundary 
(top,bottom,right,left...) but the points which show highest error is some 
what irrealted to boundary...

Do you have any idea about this? 

Always thank you for your time and advice!

Best regards,
Jaekwang Kim 



2016년 11월 2일 수요일 오후 8시 30분 19초 UTC-5, Wolfgang Bangerth 님의 말:
>
> On 11/02/2016 07:17 PM, Jaekwang Kim wrote: 
> > 
> > I'd like check the visualized error per cell. 
> > Is there any module in deal.ii that enables this...? 
> > 
>
> Yes, you just need to create a vector with as many entries as there are 
> cell 
> (e.g., the output of VectorTools::integrate_difference) and attach that to 
> the 
> DataOut object you have. step-27 shows how to do that, but it in essence 
> works 
> just like for vectors that have as many entries as there are DoFs. 
>
> Best 
>   W. 
>
> -- 
> ------------------------------------------------------------------------ 
> Wolfgang Bangerth          email:                 bang...@colostate.edu 
> <javascript:> 
>                             www: http://www.math.colostate.edu/~bangerth/ 
>
>

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