The locally stabilized finite volume method for incompressible flow

A locally stabilized finite volume method for the two-dimensional incompressible flow governed by stationary Stokes and Navier-Stokes equations is investigated in this work. A macroelement condition is introduced for constructing the local stabilized formulation for the problem. The optimal L2 error estimate of (uh, ph) determined by Stokes equations is also deduced. Some numerical examples are provided to check the efficiency of this method.