Dear Daniel,

Thank you very much! I can test my period boundary condition added truly. 
Your advision helps me a lot !

As my question is about periodic boundary condition like 

[image: 42.JPG] <about:invalid#zClosurez>
just like Dirichlet boundary condition.

But if "periodic boundary condition" means that all information of solution 
on periodic faces pair are equal, not only the value of solution (like 
Dirichlet boundary condition above), but also gradient value of solution 
(like Neuman boundary condition, as normal vector is opposite, so if 
grad_u_on_left = grad_u_on_right, for example, so n_left * grad_u_on_left + 
n_right * grad_u_on_right, top and bottom as well) . In my case, periodic 
boundary condition should include

[image: 46.JPG] <about:invalid#zClosurez>



Does deal.ii implement this kind of periodic boundary condition in fact? Is 
it different from what we have done above for periodic boundary condition 
like Dirichlet?

Thank you very much!

Best,
Chucui


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