Kyusik,

As Wolfgang already mentioned, you want to use 
FEValues::get_function_values() 
to extract from a global FE Vector the local values at the quadrature 
points in the cell you are on.
These quadrature points normally don't coincide with with the mapped unit 
support points of the
FiniteElement you are using.
Nevertheless, the global DoF indices of the local DoFs can be obtrained as 
usual by
cell->get_dof_indices()

Have a look at some of the time-dependen steps, e.g. 
step-35::assemble_one_cell_of_advection,
or just search for get_function_values in the examples folder.

Best,
Daniel

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