Sudarshan,

  When I am at the face  I need the solution at the interior  quadrature  
> points as well.  However from  dinfo1.indices   we could get the  the dof 
> indices for the cell1. But  is it possible to get the shape value at the 
> interior quadrature points ?
>
You can of course work around this by creating FEValues objects fe_values_1 
and fe_values_2 with the same quadrature rule you are using for the 
cell_integrators  and call
fe_values_1.reinit(dinfo1.cell);
fe_values_2.reinit(dinfo2.cell);
These objects can then be used to get the shape values at the interior 
quadrature points. Still it sounds weird that you would need to have these 
values. What are you trying to do?

Best,
Daniel

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