Hello Chong,

you've set `dominate = true` for your `FE_Nothing` element. This means that 
your solution will be constrained to be continuous on interfaces with other 
elements. Since `FE_Nothing` represents the zero space, all DoFs on 
interfaces will be constrained to zero.

You can disable this behavior by setting `dominate = false` (the default 
value). Correct me if I'm wrong, but I think that's what you want to do.

We've updated the documentation recently in this regard. Please see the 
`FE_Nothing 
in combination with other elements` section in the `Detailed Description` 
of FE_Nothing 
<https://www.dealii.org/developer/doxygen/deal.II/classFE__Nothing.html>.


Currently, there are other issues with the `FE_Nothing` class in 
combination with `FE_System`. Let us know if the above does not fix your 
problem and you think your issue is connected to #1496 
<https://github.com/dealii/dealii/issues/1496>.

Best,
Marc

On Tuesday, May 4, 2021 at 8:34:04 PM UTC-6 liuch...@gmail.com wrote:

> Dear Bruno
>
>
> Thank you for your reply.
>
>
> I think I did not express my problem well. To be clear, I used the 
> FE_Enriched for assigning these two finite elements and combined them using 
> FE_System:
>
> FE_Enriched<dim> fe_type_1(FE_Q<dim (1), FE_Nothing<dim>(1,true), 
> nullptr);
>
> FE_Enriched<dim> fe_type_2(FE_Q<dim (1), FE_Q<dim>(1), enriched_function);
>
> FESystem<dim> hp_FE(fe_type_1, fe_type_2).
>
>
> I would like to use fe_type_2 with an enriched_function to approximate the 
> local behavior of materials. The local behavior can be captured by the 
> extra dofs created by fe_type_2 ( note that fe_type_1 just generates the 
> standard dofs since the FE_Nothing is used). However, *I found that the 
> extra dofs are constrained when I used the make_hanging_nodes_constraints() 
> function*. The reason why I used this function is the local refinement.
>
>
> My questions are
>
> (1) Is there a way to keep the extra dofs introduced by fe_type_2 
> unconstrained when applying the make_hanging_nodes_constraints() function?
>
>
> (2) If the extra dofs require to constrain when the 
> make_hanging_nodes_constraints() function is utilized, can I remove these 
> extra dofs from the AffineConstraints container generated by the function?
>
>
> Hope I express my problems clearly. Thank you for any suggestions.
>
>
> Best wishes,
>
> Chong
>
> Bruno Turcksin <bruno.t...@gmail.com> 于2021年5月5日周三 上午2:21写道:
>
>> Chong Liu,
>>
>> On Tuesday, May 4, 2021 at 12:06:39 PM UTC-4 liuch...@gmail.com wrote:
>>
>>>
>>> Question:
>>>
>>> *How can I only constrain the hanging nodes for fe_type_1*? 
>>>
>>
>> Why do you want to do that? If you don't constrain fe_type_2, the 
>> solution won't be continuous. If you have more dofs in one side of the edge 
>> than in the other side, you need to constrain some of the dofs. It doesn't 
>> matter if the reason you have more dofs is because the cell has been 
>> refined or if it's because the fe degree is higher.
>>
>> Best,
>>
>> Bruno
>>
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