A combined characteristic-based split algorithm and an adaptive meshing technique for analyzing two-dimensional viscous incompressible flow are presented. The method uses the three-node triangular element with equal-order interpolation functions for all variables of the velocity components and pressure. The main advantage of the combined method is that it improves the solution accuracy by coupling an error estimation procedure to an adaptive meshing technique that generates small elements in regions with a large change in solution gradients, and at the same time, larger elements in the other regions. The performance of the combined procedure is evaluated by analyzing one test case of the flow past a cylinder, for their transient and steady-state flow behaviors.