Spatiotemporal patterns that appear during the electrodissolution of a metal that exhibits passivity are simulated by a two-variable model in a three-dimensional geometry with a point like reference electrode. The dynamical variables of the model are the potential drop across the electric double layer and the proton concentration in front of the working electrode surface. The simulations elucidate the role of the geometry of the electrode arrangement in an electrochemical cell and of experimental parameters in the evolution of patterns like rotating waves on a ring electrode, spatially homogeneous oscillations or a non-uniform stationary state including transitions between them. The prevalence of a specific spatiotemporal pattern is controlled by the interplay of positive and negative long-range coupling of sites on the electrode through the electric field. The model is of a general character and does not take into account the specific kinetics of a given metal.