Junchao,

>> The interpolated solution should already have the correct (old) boundary 
>> conditions.
>>
> Is it true? As you see, I call 
> constraints.distribute(interpolated_solution) to impose boundary 
> constraints, which are computed in setup_system() as follows
>
What I meant to say is that the interpolated vector has the old boundary 
values if you don't apply additional constraints.
On cells that you refine, you can improve the approximation of the boundary 
values by applying a ConstraintMatrix (at time-dt) and hanging node 
constraints.

For the current time step, you then initialize a different ConstraintMatrix 
containing both Dirichlet boundary values (at time instead of time-dt) and 
hanging node constraints
and use this when assembling your system.

Best,
Daniel

>

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