  We apply the piecewise constant, discontinuous Galerkin method to discretize
a fractional diffusion equation with respect to time. Using Laplace transform
techniques, we show that the method is first order accurate at the \$n\$th time
level \$t_n\$, but the error bound includes a factor \$t_n^{-1}\$ if we assume
no smoothness of the initial data. We also show that for smoother initial data
the growth in the error bound as \$t_n\$ decreases is milder, and in some cases
absent altogether. Our error bounds generalize known results for the classical
heat equation and are illustrated for a model problem.
