Discrete-time Galerkin methods are considered for the approximate solution of a parabolic initial boundary value problem which arises, for example, in problems involving the diffusion of a solute into a solid from a stirred solution of fixed volume. Optimal error estimates in the L2 and H1 norms are derived for the Crank-Nicolson Galerkin method. For the one space variable case optimal L∞ estimates are also obtained. Results of numerical experiments are presented and comparisons with finite difference approximations are made.