In this paper we extend the introductory work described in the accompanying papers on the use of adaptive finite element methods in electrochemical simulation (K. Harriman et al., Electrochem. Commun. 2 (2000) 150 and 157) to the case of a (pseudo) first-order EC' reaction mechanism at both an inlaid and a recessed disc. The recessed disc is shown to be a particularly suitable example for illustrating the power of the technique in providing the simulated current to a guaranteed accuracy on near-optimal meshes. For both problems we demonstrate that we can obtain excellent accuracy across the spectrum of reaction rates using just a few seconds of CPU time. Our results also confirm the accuracy of some recently published analytical solutions to these problems (L. Rajendran, M.V. Sangaranarayanan, J. Phys. Chem. B 103 (1999) 1518-1524; J. Galceran et al., J. Electroanal. Chem. (1999) in press). (C) 2000 Elsevier Science S.A.