Hi,

Well, I found that the FiniteElement base class itself has a method 

Tensor< 1, dim > FiniteElement< dim, spacedim >::shape_grad (const unsigned 
int i, const Point<dim> &p) const

which can compute shape gradient values at a given point, but the result it 
get is on the reference cell, not the real cell. And it has an additional 
condition says that "*Implementations of this function should throw an 
exception of type ExcUnitShapeValuesDoNotExist if the shape functions of 
the FiniteElement under consideration depend on the shape of the cell in 
real space, i.e., if the shape functions are not defined by mapping from 
the reference cell*", which I don't quite understand.

I will try to start from this method, but I still hope someone could give 
some better ideas? Thanks for your reading!

Best regards,
David.

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