We propose new ways of computing the stabilization parameters used in the stabilized finite element methods such as the streamline-upwind/Petrov–Galerkin (SUPG) and pressure-stabilizing/Petrov–Galerkin (PSPG) formulations. The parameters are computed based on the element-level matrices and vectors, which automatically take into account the local length scales, advection field and the Reynolds number. We describe how we compute these parameters in the context of first a time-dependent advection–diffusion equation and then the Navier–Stokes equations of unsteady incompressible flows.