Dear Prof. Bangerth:

Thank you very much for your quick reply! 

When I apply hanging node constraints to my matrix, as the step-6 
says: https://www.dealii.org/developer/doxygen/deal.II/step_6.html
I make 4 steps:
    1.Create a Constraints Class:
ConstraintMatrix     constraints;

    2.Fill this object using the function 
DoFTools::make_hanging_node_constraints() to ensure continuity of the 
elements of the finite element space.
DoFTools::make_hanging_node_constraints (dof_handler,
                                           constraints);

    3.Copy the local contributions to the matrix and right hand side into 
the global objects:
      constraints.distribute_local_to_global (cell_matrix,
                                              cell_rhs,
                                              local_dof_indices,
                                              system_matrix,
                                              system_rhs);
      constraints.distribute_local_to_global (cell_volume_matrix,
                                              local_dof_indices,
                                              volume_matrix);    
      constraints.distribute_local_to_global (cell_gradient_matrix,
                                              local_dof_indices,
                                              gradient_matrix); 


    4.Make sure that the degrees of "freedom" located on hanging nodes get 
their correct (constrained) value:
 constraints.distribute (solution);

So I don't know which step I use incorrectly? And the version of deal.ii I 
use is 8.5.1, which doesn't have the updated class AffineConstraints 
<number>, but have Constraint_matrix Class. I don't know if this is the key 
point. Need I update my deal.ii?

Thank you very much!

Best,
Chucui

在 2019年2月11日星期一 UTC+8下午1:40:07,Wolfgang Bangerth写道:
>
> On 2/10/19 8:20 PM, [email protected] <javascript:> wrote: 
> > 
> > And the results without adaptive mesh seem like approximate the exact 
> results 
> > correctly. So I am confused why the results of "grad u square" with 
> adaptive 
> > mesh are so strange? 
>
> I suspect that you forget to apply hanging node constraints to your 
> matrix, or 
> apply them incorrectly -- which is exactly why I asked you to try globally 
> refined meshes: they don't have hanging node constraints :-) 
>
> Best 
>   W. 
>
> -- 
> ------------------------------------------------------------------------ 
> Wolfgang Bangerth          email:                 [email protected] 
> <javascript:> 
>                             www: http://www.math.colostate.edu/~bangerth/ 
>
>

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