A Mesh Superposition Technique (MST) for the progressive transition between differently-discretized subdomains is proposed and implemented in an FE code. The interfaces between these subdomains are replaced by transition regions where the corresponding meshes are superposed. The MST is applied to the multiple length/time-scale analysis of a low-velocity impact of a projectile on a composite plate. Unlike using a sudden discretization-transition approach, the use of the MST eliminates the undesirable stress disturbances at the interface between differently-discretized subdomains and, as a result, it correctly captures the impact-induced damage pattern at a lower computational cost. Finally, the MST is coupled with an implicit/explicit co-simulation technique for a multiple time/length-scale analysis. The results indicate that, if the length-scale transition is performed using the proposed MST instead of a sudden discretization-transition, the CPU time can be nearly halved.