We discuss the Navier-Stokes equations (NS equations) and the implementation of a well-known least squares finite element algorithm in an object-oriented framework. We review the conjugate gradient method (CG method) utilized in solving the least-squares formulation as well as the corresponding key components specific to the application of the CG method with respect to the NS equations and the natural application of the finite element method resulting from the components. We discuss the application of the implemented solver toward several standard benchmarks, we visualize benchmark results, and we discuss computational aspects of the implemented solver with respect to benchmark results.