Cellwise interpolation of a discontuous function onto a (possibly nonmatching) mesh

DG-1 will be very tricky to capture accurately, as you will have multiple dofs at the same physical position, which the algorithm cannot logical distinguish.

If you want something discontinuous transfered, i would either:

  1. use a projection, as described here:
    L2 projection of fine mesh solution to a coarse mesh - #6 by dokken
  2. use DG-0, whose coordinate is at the cell center, and does not have duplicates.