The applications of a finite element scheme to three-dimensional incompressible viscous fluid flows are presented. The scheme is based on the Petrov-Galerkin weak formulation with exponential weighting functions. The incompressible Navier-Stokes equations are numerically integrated in time by using a fractional step strategy with second-order accurate Adams-Bashforth scheme for both advection and diffusion terms. Numerical solutions for flow around a circular cylinder up to high Reynolds numbers are presented.