We do allow hanging nodes. You are refering to a subset of the literature on
adaptive methods, namely the subset of people using bisection.

Best,
G

Yujie wrote:
> Hello, Everyone
> 
> Maybe, my question is very simple. However, I can't find some references to
> demonstrate it. I wish I could get some help from here. The question is
> about hanging nodes after mesh refinement. From the mesh, I can directly
> understand what the hanging node is. However, I can't clearly understand why
> the hanging node is not permitted in finite element method. The answer in
> most of the papers about adaptive mesh refinement is to keep the conformity
> of the mesh. However, are there good examples to show this effect if the
> hanging node is not processed. Thanks a lot.
> 
> Regards,
> Yujie
> 
> 
> 
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