Abstract: "Local uniform grid refinement (LUGR) is an adaptive- grid technique for computing solutions of partial differential equations possessing sharp spatial transitions. Using nested, finer-and-finer uniform subgrids, the LUGR technique refines the space grid locally around these transitions, so as to avoid discretization on a very fine grid covering the entire physical domain. This paper examines the LUGR technique for time-dependent problems when combined with static-regridding. Static-regridding means that in the course of the time evolution the space grid is adapted only at discrete values of time.