Jarkwang,

Quadrature points and support points only coincide in special cases. In 
particular, this not true for Gauss quadrature of order fe_degree+1 and FE_Q 
elements.

When computing errors, you often want to avoid superconvergence effects and 
hence use a quadrature rule different from the one chosen for assembling system 
matrix and right-hand side. Have a look at the discussion in step-7 [1] for 
this.

Best,
Daniel

[1] 
https://www.dealii.org/8.4.1/doxygen/deal.II/step_7.html#Verificationofcorrectness

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