Thanks for the reply, 

I just wanted to make sure that whether I implemented it right, 
but I still cannot sure whether I am doing correctly..... Let me be with 
more specific questions. 

First, Yes I am considering 2-dimensional flow.
if I writes a code that looks as previous, 

template <int dim>

  void

  RightHandSide<dim>::vector_value (const Point<dim> &p,

    Vector<double>   &values) const

  {

    values(0) =  pow(p[0],2);  

    values(1) =  pow(p[1],2);

   * values(2) =  0.0;  // I assumed this always zero. because f is 2 
dimensional force, and we will not have third component of f*. 

  }

1) whether my interpretation of 'values(2) is correct' - marked with red 
line 

2) If we considered a vector value test function phi=(*v,*q)= (v_x, v_y , 
q), the right hand side term in weak form should look like this 

RHS = (*v, f* ) at domain o mega. 

since both *v* and* f* is vector that has two direction , (x and y) , the 
calculation should be conducted in both direction 
but in the following code, it seems that I am multiplying only the first 
component v and f... 
Do I understand this appropriately?

In this sense, I don't understand my code well... cuz it looks like...

*const unsigned int component_i =*

*   fe.system_to_component_index(i).first;   <- Here I only said the first *
*component...*

* local_rhs(i) += fe_values.shape_value(i,q) **

* rhs_values[q](component_i) **

* fe_values.JxW(q);*


Shouldn't this be some thing like this?  

*const unsigned int component_i =*

*   fe.system_to_component_index(i).first; *

*const unsigned int component_j = *

*                  fe.system_to_component_index(j).second; *

* local_rhs(i) += (fe_values.shape_value(i,q) **
*rhs_values[q](component_i)) *

                                *(fe_values.shape_value(i,q) **
*rhs_values[q](component_j)) *
* fe_values.JxW(q);* 

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