In this computational study, the convergence, stability and order of accuracy of several different numerical schemes are assessed and compared. All of the schemes considered were developed using a normalized variable diagram. Two test cases are considered: (1) two-dimensional steady incompressible laminar flow of a Newtonian fluid in a square lid-driven cavity; and (2) creeping flow of a PTT-linear fluid in a lid-driven square cavity. The governing equations are discretized to varying degrees of refinement using uniform grids, and solved by using the finite volume technique. The momentum interpolation method (MIM) is employed to evaluate the face velocity. Coupled mass and momentum conservation equations are solved through an iterative SIMPLE (Semi-Implicit Method for Pressure-Linked Equation) algorithm. Among the higher-order and bounded schemes considered in the present study, only the CLAM, COPLA, CUBISTA, NOTABLE, SMART and WACEB schemes provide a steady converged solution to the prescribed tolerance of $1{ imes}10^{-5}$ at all studied Weissenberg ($We$) numbers, using a very fine mesh structure. It is found that the CLAM, COPLA, CUBISTA, SMART and WACEB schemes provide about the same order of accuracy that is slightly higher than that of the NOTABLE scheme at low and high Weissenberg numbers. Moreover, flow structures formed in the cavity, $i.e.$ primary vortex, are captured accurately up to $We$ = 5 by all converged schemes.