We present a formulation for incompressible ﬂows analysis using the ﬁnite element method (FEM). The necessary stabilization for dealing with convective eﬀects and the incompressibility condition is modeled via the ﬁnite calculus (FIC) method. The stabilization terms introduced by the FIC formulation allow to solve a wide range of ﬂuid ﬂow problems for low and high Reynolds numbers ﬂows without the need for a turbulence model. Examples of application of the FIC/FEM formulation to the analysis of 2D and 3D incompressible ﬂows with moderate and large Reynolds numbers are presented. Ó 2007 Elsevier Inc. All rights reserved.