When applying HR for a cell C, on each hierarchical stage one needs to compute cell averages on neighboring cells and remove the contribution of the updated remainder term on cell C from these cell averages. This requires the updated remainder term on cell C to be averaged over neighboring cells. It is here where a mistake is easily made, to average updated remainder terms (other than the one defined on cell C) on their corresponding cells, which degenerates the order of accuracy to second order.