Hi, all 

I have a question on using deal.ii for solving unknown boundary condition 
I have thought the most minimized related to my question. 

where I consider a navies slip boundary condition, and I have tried to 
solve this with finite difference.
For more demonstration please see following screenshot. 


Finite Difference Formulation might be...


where the last raw of matrix is added to show boundary condition at lower 


and I think problem is generally well posed so that I can solve this with 


Now, I am trying to solve same problem using finite element method...


The description of same boundary condition in weak form will look like 


 has on the boundary


        for (unsigned int face=0; face<GeometryInfo<dim>::faces_per_cell; 

        { if (cell->face(face)->boundary_id() == 2)

            {  for (unsigned int q=0; q<n_face_q_points; ++q)

                { for (unsigned int i=0; i<dofs_per_cell; ++i)

                    {for (unsigned int j=0; j<dofs_per_cell; ++j)

                        {cell_matrix(i,j) += (1/beta)*fe_values.shape_value 
(i, q_index)*

                                                fe_values.shape_value (j, 

                                                * fe_face_values.JxW(q);}

                            cell_rhs(i) += 0;

                    }//i cycle

                }//quadrature (face) cycle


        }//end of face cycle




and I think I should add this cell_matrix(i,j) and cell_rhs(i) to my system 

but not overlapping the rows that describe weakform of original poisson 
equation.. so I think i should not use them...

   for (unsigned int i=0; i<dofs_per_cell; ++i)


            for (unsigned int j=0; j<dofs_per_cell; ++j)

                system_matrix.add (local_dof_indices[i],




                system_rhs(local_dof_indices[i]) += cell_rhs(i);


In this situation, how should I expand (to add rows) my system matrix and 
connect to it boundary dof ? 


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