A least-squares finite element method for the Navier–Stokes equations

The Navier–Stokes equations for flow in a plane are reformulated as a first-order system in terms of stress and stream functions. Solutions of this system are obtained by the least-squares finite element method. A feature of this approach is that the linearised system gives rise to a symmetric and positive-definite linear algebra problem at each Newton iteration. Care over handling the incompressibility term is needed to ensure good results are obtained.