The problem of numerical simulation of the current to a microdisc electrode is made difficult by the presence of a boundary singularity at the electrode edge, which causes large errors in the simulated concentration values, and consequently in the simulated flux at the electrode. We describe some simple and easily implemented strategies for deriving a refined mesh that will overcome this problem. We take as our model problem steady-state diffusion to a stationary microdisc electrode, for which the full analytic solution is known, since this allows us to demonstrate the accuracy of the numerical approximations. By making a detailed study of the causes of error in the flux calculation, we are able to show how error cancellation can be used to obtain an exponentially expanding mesh on which the flux can be evaluated to any desired degree of accuracy.