Abstract: Complex geometry problems may require the use of non-structured grids, which has greater computational effort than presented in structured mesh. However, the latter strategy is hard to adapt to the general complex domain. In order to get a faster computational code and retaining the adaptivity of the non-strutured grid, a mixed scheme is proposed. The present scheme is tested for the driven cavity problem, which is extensively used as a benchmarck problem to evaluate numerical techniques that solve the Navier-Stokes equations. The incompressible fluid is integrated by calculating the velocity fields and computing the pressure field in each time step following the schemes used previously (Plate et all., 1998).