How accurate is your two-dimensional numerical simulation? .1. An introduction

Numerical simulations of the diffusion processes at electrode surfaces are subject to three sources of error: those arising in the calculation of the concentration values, those arising in the numerical approximation of the flux at the electrode surface, and those arising from the integration of the flux over the electrode surface. In this paper we investigate the effects of each type of error on the accuracy of numerical simulation at the microdisc electrode by solving the steady state problem (for which the analytical solution is known). We are able to show that the major source of error is due to the boundary singularity at the electrode edge. By introducing a simple model problem, we demonstrate that the theoretical rates of convergence of the standard finite difference schemes can be attained in the absence of a boundary singularity, but these rates are destroyed by the presence of the singularity when solving for the electrode problem. Finally, we show that it is not possible to recover accuracy using n-point flux calculations or spline functions at the electrode edge.