I have encountered the term cell "Cell averaged derivatives" and "Taylor series expansion using cell averaged derivatives about centroid" in the context of polynomial representation in any cell (computational element with some higher order interpolation polynomial nodes).
Here is the link to the below paper: http://dept.ku.edu/~cfdku/papers/AIAA-2009-605.pdf
I have also read the reference of this reference paper http://people.math.gatech.edu/~yingjie/publications/centr_DG_ovlpcell_new_iii.pdf Section 4.1
I tried to find alternate references and easier sources of explanation, but everywhere it has been mentioned that the coefficients of the above Taylor series expansion can be found easily.
However, I am still unable to grasp the procedure properly. It would be nice if someone could help me understand which seems to be trivial for everyone.