hi all,

I would like to ask whether it is 
possible to implement neumann boundary condition and dirichlet boudary 
condition to the same boundary.

I tried it but unfortunately it did not fulfilled, I mean that dirichlet 
boundary condition was fulfilled 
but neumann wasn't. I checked neumann from the derivative of the 
solution.

I used for dirichlet the same as in the examples:

 {
    std::map<unsigned int,double> boundary_values;
    
    VectorTools::interpolate_boundary_values (dof_handler,
                          bi,
                          *BC_Function,
                          boundary_values);
    
    MatrixTools::apply_boundary_values (boundary_values,
                   system_matrix,
                        solution,
                        system_rhs);
      }


and neumann

{
            double JxW = fe_face_values.JxW(q_point);
            for (unsigned int i=0; i<dofs_per_cell; ++i)
              cell_rhs(i) += ( neumann_val *
                     fe_face_values.shape_value(i,q_point) * JxW);
          }



any helful comments will be appreciated.


best regards,
ahmad
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