In this article, we present a new approach for the numerical simulation of electrochemical problems based on an idea, which can be defined as a ‘geometrically adaptive approach’. It is based on the decomposition of the simulation domain into adjoining patches whose shape, size and grid meshes are adjusted individually to account for specific expected difficulties imposed by geometric constraints of the electrochemical system. The validity and the efficiency of this new technique are established through its successful application to the problem of diffusion at the microdisk, i.e. to the diffusional problem in which the conflicting difficulties between diffusion and the heterogeneity of current density at the edge of the disk are the most severe. The ensuing simulated current obtained through the Hopscotch finite-difference method is compared to previously published analytical approximations and to former numerical results obtained by different numerical approaches. The method is thus shown to be stable, extremely precise and reliable though it requires a minimum computation time and memory occupation, especially when it is coupled with a non-uniform exponentially expanding time grid.