This paper concerns a new class of robust and efficient methods for solving the Navier–Stokes equations for unsteady incompressible flow. In previous work we established the effectiveness of an implicit time integrator using a stabilized trapezoid rule with an explicit Adams–Bashforth method for error control. The role of the stability of the spatial approximation on the overall accuracy of the implicit solution algorithm is the primary focus here. In particular, the relationship between spatial stabilization and temporal solution accuracy is assessed computationally for the case of the lowest order conforming mixed approximation. Copyright © 2012 John Wiley & Sons, Ltd.