Hi Kyusik,

What makes me confused here is that, according to your explanation, two 
> different DoFHandler could be used simultaneously.
>

Yes, that it correct. You can convert between cell iterators. So I do the 
following:

          typename Triangulation<dim>::active_cell_iterator
          cell = triangulation.begin_active(),
          endc = triangulation.end();
          for (; cell!=endc; ++cell)
          {
            const typename DoFHandler<dim>::active_cell_iterator cell_1 
(&triangulation, cell->level(), cell->index(), &dof_handler_1);
            typename DoFHandler<dim>::active_cell_iterator cell_2 
(&triangulation, cell->level(), cell->index(), &dof_handler_2);
          ...}

and then follow the usual process of FEValues reinitialisation
 

> Also, It seems that I have to use two different FEValues<dim> one for 
> solution the other for the vector...
>

Yes you would need to. The one relates to the scalar FE system and the 
other to the new vector FE system.
 

> In the assemble_system() for M and f, can I use these two things 
> simultaneously...?
>

Sure. You use one for assembly and one for the extraction of gradient data 
from the scalar solution field.

Regards,
Jean-Paul
 

>
> Thank you
>
> Kyusik.
>
>  
>

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