Hello, 

It's been a while since I asked questions to this group, and I hope you are 
all doing well
I tried to figure this out and dug into the communications, but failed, so 
if anyone can help me, I would greatly appreciate it. 

I know the deal.ii has this information and I know I have to use 
" MappingQ1<dim,dim> mapping; "..

1. Is there any way to get or access to the reference element basis 
functions? 
e.g \hat{phi}_i  (\hat{x}) where \hat{x} \in \hat{K} 

2. In the other direction, I calculated the reference element basis 
functions with hand, and I want to use the "transform" 
(https://www.dealii.org/current/doxygen/deal.II/classMapping.html)

virtual void Mapping< dim, spacedim >::transform 
(const ArrayView< const Tensor< 1, dim > > & input,
const MappingKind kind,
const typename Mapping< dim, spacedim >::InternalDataBase & internal,
const ArrayView< Tensor< 1, spacedim > > & output 
) 

But, I don't think we have public acces to "const typename Mapping< dim, 
spacedim >::InternalDataBase &  internal," so I am keep failing. 

Any advice/idea or your example would be a great help for me. 

Thanks

Sanghyun Lee
Florida State University

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