Electrodeposition of a metal into rectangular cross-section trenches by the application of a current or potential step is investigated via numerical simulations. The feasibility of decoupling of the phenomena occurring on scales of the trench filling time and the species diffusion time is examined. Short time scale events under potentiostatic plating conditions are compared with those events that occur under galvanostatic conditions. Two numerical schemes, the finite volume method (FVM) and the boundary element method (BEM), are used in solving the unsteady diffusion problems. Furthermore, unsteady diffusion with nonlinear reaction rate kinetics on the cathode is considered.