Thank you very much your kind reply.

Could I have one more question..?
 
You mention that

>
> The difference that in step-3, you are imposing *strong* boundary 
> conditions, 
> whereas in step-20, you are imposing *weak* boundary conditions. 
>
>
Then, is there anyway to use strong boundary condition using FESystem<dim>

Because, It seems that the below thing, that I added in step-20, doesn't 
work out.

    //test for strong boundary condtion
      std::map<types::global_dof_index,double> boundary_values_strong;
      VectorTools::interpolate_boundary_values (dof_handler,
                                                0,
                                                ZeroFunction<dim>(),
                                                boundary_values_strong);
      MatrixTools::apply_boundary_values (boundary_values_strong,
                                          system_matrix.block(1,1),
                                          solution.block(1),
                                          system_rhs.block(1));
    //test for strong boundary condtion

The error message is...

An error occurred in line <1783> of file 
</user2/hanks318/dealii/dealii-8.3.0/include/deal.II/numerics/vector_tools.templates.h>
 
in function
    void 
dealii::VectorTools::<unnamed>::do_interpolate_boundary_values(const 
M_or_MC<DH::dimension, DH::space_dimension>&, const DH&, const typename 
dealii::FunctionMap<DH::space_dimension, double>::type&, std::map<unsigned 
int, double, std::less<unsigned int>, std::allocator<std::pair<const 
unsigned int, double> > >&, const dealii::ComponentMask&, 
dealii::internal::int2type<dim_>) [with DH = dealii::DoFHandler<2, 2>, 
M_or_MC = dealii::Mapping, int dim_ = 2]
The violated condition was:
    n_components == i->second->n_components
The name and call sequence of the exception was:
    ExcDimensionMismatch(n_components, i->second->n_components)
Additional Information:
Dimension 3 not equal to 1

Stacktrace:
-----------
#0  /user2/hanks318/dealii/dealii_pre/lib/libdeal_II.g.so.8.3.0:
#1  /user2/hanks318/dealii/dealii_pre/lib/libdeal_II.g.so.8.3.0: void 
dealii::VectorTools::interpolate_boundary_values<dealii::DoFHandler<2, 2> 
>(dealii::Mapping<dealii::DoFHandler<2, 2>::dimension, 
dealii::DoFHandler<2, 2>::space_dimension> const&, dealii::DoFHandler<2, 2> 
const&, dealii::FunctionMap<dealii::DoFHandler<2, 2>::space_dimension, 
double>::type const&, std::map<unsigned int, double, std::less<unsigned 
int>, std::allocator<std::pair<unsigned int const, double> > >&, 
dealii::ComponentMask const&)
#2  /user2/hanks318/dealii/dealii_pre/lib/libdeal_II.g.so.8.3.0: void 
dealii::VectorTools::interpolate_boundary_values<dealii::DoFHandler<2, 2> 
>(dealii::Mapping<dealii::DoFHandler<2, 2>::dimension, 
dealii::DoFHandler<2, 2>::space_dimension> const&, dealii::DoFHandler<2, 2> 
const&, unsigned char, dealii::Function<dealii::DoFHandler<2, 
2>::space_dimension, double> const&, std::map<unsigned int, double, 
std::less<unsigned int>, std::allocator<std::pair<unsigned int const, 
double> > >&, dealii::ComponentMask const&)
#3  /user2/hanks318/dealii/dealii_pre/lib/libdeal_II.g.so.8.3.0: void 
dealii::VectorTools::interpolate_boundary_values<dealii::DoFHandler<2, 2> 
>(dealii::DoFHandler<2, 2> const&, unsigned char, 
dealii::Function<dealii::DoFHandler<2, 2>::space_dimension, double> const&, 
std::map<unsigned int, double, std::less<unsigned int>, 
std::allocator<std::pair<unsigned int const, double> > >&, 
dealii::ComponentMask const&)
#4  ./step-20: Step20::MixedLaplaceProblem<2>::assemble_system()
#5  ./step-20: Step20::MixedLaplaceProblem<2>::run()
#6  ./step-20: main
--------------------------------------------------------

Thank you.

Kyusik.

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