Thanks a lot, Bruno! Using build_patches(2) on the coarse mesh (I am using 
linear elements) the two interpolations look much more alike.

Since I will need to do the same transformation several times for different 
vectors, I am coming back to my other question: Is there a function that 
uses the std::vector<std::map<.,.>> of 
DoFTools::commpute_intergrid_transfer_
representation and makes some sort of transfer matrix from it? According to 
the documentation, there is such a function. But according to the docu, the 
output of compute_intergrid_transfer_representation is still a matrix so I 
am not sure if I just missed it or if it does not exist since the docu is 
out of date. 

Best,
Ina

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