First-order system least squares for the Oseen equations

Following earlier work for Stokes equations, a least-squares functional is developed for twoand three-dimensional Oseen equations. By introducing a velocity flux variable and associated curl and trace equations, ellipticity is established in an appropriate product norm. The form of Oseen equations examined here is obtained by linearizing the incompressible Navier-Stokes equations. An algorithm is presented for approximately solving steady state, incompressible Navier-Stokes equations with a Nested Iteration-Newton-FOSLS-AMG iterative scheme, which involves solving a sequence of Oseen equations. Some numerical results for Kovasznay flow are provided.