At the moment, the coarsening method basically places a whole cell into a broader cell, or none of it. It would be better if it used a fraction of the cell proportional to how much of it is in the broader cell.
Note that it still averages down properly, because each cell is averaged by the number of cells falling into it. However, there will be fewer edge effects if the fractional cells can be accounted for.
At the moment, the coarsening method basically places a whole cell into a broader cell, or none of it. It would be better if it used a fraction of the cell proportional to how much of it is in the broader cell.