A least-squares finite element method for incompressible flow in stress-velocity-pressure version Original Research Article

In this paper we are concerned with the incompressible flow in 2-D. Introducing additional variables of derivatives of velocity, which are called stresses here, the second-order dynamic equations are reduced into a first-order system with variables of stress, velocity and pressure. Combining the compatability conditions: and the divergence ice condition, we have a system with six first-order equations and six unknowns. Least-squares method performed over this extended system. The analysis shows that this method achieves optimal rates of convergence in the H1-norm as the h approaches to zero. Numerical experiences are also available.