Since
since my question include some mathematical expression, I attached figure 
for this...

<https://lh3.googleusercontent.com/-sf5E7jwOi8c/WUFw9_TpW_I/AAAAAAAABBw/mYzXd17TU_I1NU9T6Thr5AMoMFZcRFj1ACLcBGAs/s1600/Screen%2BShot%2B2017-06-14%2Bat%2B12.21.40%2BPM.png>



















 copy_data.cell_matrix(i,j) += (

                                           

                                           (advection_directions[q_point] * 
scratch_data.fe_values.shape_grad(j,q_point)   *

                                           
(scratch_data.fe_values.shape_value(i,q_point) +

                                            

                                            delta *

                                             (advection_directions[q_point] 
*

                                              
scratch_data.fe_values.shape_grad(i,q_point)))

                                            

                                            //add diffusion term - should I 
consider stabilization term for this one too? Lets see.

                                            
+scratch_data.fe_values.shape_grad(i,q_point) 
*  scratch_data.fe_values.shape_grad(j,q_point)         

                                            //stabilization term for 
diffusion

                                            // (delta)(nabla^2 u , beta . 
nabla v)

                                            +delta * ( - 
scratch_data.fe_values.shape_grad(j,q_point) * 
scratch_data.fe_values.shape_grad(j,q_point) )

                                                   * 
(advection_directions[q_point] * 
scratch_data.fe_values.shape_grad(i,q_point) )

                                            

                                            ) *

                                           
scratch_data.fe_values.JxW(q_point));


but, I am not receiving solution I expected (it has manufactured 
solution...)

Is this approach wrong? or the direction is just correct, but I am making 
mistake somewhere in my code 


Thanks 

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