A recently described adaptive multilevel finite element algorithm with error control of the concentrations and the electrochemical response variable, here the electrode potential, is applied to the simulation of various controlled-current (chronopotentiometric) experiments. In particular. cases with singularities in the initial values of the unknowns or in the excitation function are treated. Electron transfers of both, dissolved and adsorbed, species are considered. Results of numerical calculations are compared to analytical solutions. Limitations of the numerical algorithms are discussed. (c) 2007 Elsevier B.V. All rights reserved.