We present a simple filtering procedure for stabilizing the spectral elemen
t method (SEM) for the unsteady advection-diffusion and Navier-Stokes equat
ions. A number of example applications are presented, along with basic anal
ysis for the advection-diffusion case. (C) 2001 Academie des sciences/Editi
ons scientifiques et medicales Elsevier SAS.