The wave concept of group (or energy) velocity is used to predict how errors propagate in three numerical schemes for the solution of the diffusion equation with flow and decay. A five–point filter is used to isolate the long and the saw–tooth grid–scale errors. Contour plots are presented which illustrate the markedly different propagation of the long and saw–tooth errors. The energy of long errors is carried downstream with the flow. An illustrative example is given for which, as predicted, the saw–tooth errors go upstream.