We present a collection of stabilized finite element (FE) methods derived via first‐ and second‐order finite calculus (FIC) procedures. It is shown that several well known existing stabilized FE methods such as the penalty technique, the Galerkin Least Square (GLS) method, the Pressure Gradient Projection (PGP) method and the orthogonal sub‐scales (OSS) method are recovered from the general residual‐based FIC stabilized form. A new family of stabilized Pressure Laplacian Stabilization (PLS) FE methods with consistent nonlinear forms of the stabilization parameters are derived. The distinct feature of the family of PLS methods is that they are residual‐based, i.e. the stabilization terms depend on the discrete residuals of the momentum and/or the incompressibility equations. The advantages and disadvantages of the different stabilization techniques are discussed and several examples of application are presented.