Thanks for the response! 

I tried to put "Assert (system_matrix.n() == dof_handler.n_dofs(), 
ExcInternalError()); " when I assemble system , but i get the same error 
message, regardless of it 

*An error occurred in line <1668> of file 
</Users/kimjaekwang/dealii-8.4.1/include/deal.II/lac/constraint_matrix.templates.h>
 
in function*

*    void dealii::internals::dealiiSparseMatrix::add_value(const LocalType, 
const size_type, const size_type, SparseMatrixIterator &) 
[SparseMatrixIterator = dealii::SparseMatrixIterators::Iterator<double, 
false>, LocalType = double]*

*The violated condition was: *

*    matrix_values->column() == column*

*The name and call sequence of the exception was:*

*    typename SparseMatrix<typename 
SparseMatrixIterator::MatrixType::value_type>::ExcInvalidIndex(row, column)*

*Additional Information: *

*You are trying to access the matrix entry with index <3,13>, but this 
entry does not exist in the sparsity pattern of this matrix.*




By the way, i found that the code is working well when I refine my mesh 
globally, saying 100% of refinement. 



GridRefinement::refine_and_coarsen_fixed_number (triangulation,

                                                     
estimated_error_per_cell,

                                                     1.0, 0.0); 




it goes 5-refinement cycle perfectly. 


*Cycle 0:*

*   Number of active cells:       4*

*   Number of degrees of freedom: 25*

*dof_hander._n_dofs() : 25*

* Assemble system finished*

*   ||u_k-u_{k-1}|| = 9.91167e-06   Iteration Number: 52*

*   L2_error : 0.00233134*

*Cycle 1:*

*   Number of active cells:       16*

*dof_hander._n_dofs() : 81*

*Set up system finished*

* Assemble system finished*

*   ||u_k-u_{k-1}|| = 9.41577e-06   Iteration Number: 15*

*   L2_error : 0.000299119*

*Cycle 2:*

*   Number of active cells:       16*

*dof_hander._n_dofs() : 81*

*Set up system finished*

* Assemble system finished*

*   ||u_k-u_{k-1}|| = 9.98969e-07   Iteration Number: 2*

*   L2_error : 0.000287962*

*Cycle 3:*

*   Number of active cells:       16*

*dof_hander._n_dofs() : 81*

*Set up system finished*

* Assemble system finished*

*   ||u_k-u_{k-1}|| = 6.38877e-06   Iteration Number: 1*

*   L2_error : 0.000287717*

*[100%] Built target run*



However, if only 90% of cell is being refined, I could only go 3 cycle, 

and if then same of less than 80 I am receiving same errors... 

Might AMR be related to this...?



GridRefinement::refine_and_coarsen_fixed_number (triangulation,

                                                   
  estimated_error_per_cell,

                                                     0.8, 0.0); 



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