AbstractRecently, a rigorousa posteriorierror estimate, based on the element residual method, for the steady‐state Navier‐Stokes equations has been derived. In this paper, by using this error estimate, we construct anhpadaptive strategy to minimize the total computation costs while achieving a targeted accuracy for steady incompressible viscous flow problems. The basichpadaptive strategy is to solve the approximate problem in three consecutive stages corresponding to three different meshes, i.e. an initial mesh, an intermediate adaptiveh‐mesh, and a final adaptivehpmesh. Our numerical result shows that the three‐stephpadaptive strategy for the incompressible flow problems indeed provides an accurate approximate solution while keeping the computational costs under