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The focus of this contribution is the examination of the influence of different interpolation orders (especially for the pressure field) by solving the stationary incompressible Navier-Stokes equations with least-squares finite elements. We consider two different div-grad first-order systems which result in a three-field formulation with stresses, velocitites and pressure, see e.g. SCHWARZ & SCHRÖDER [1] and BOCHEV & GUNZBURGER [2]. Additionally, a numerical example is presented to show the performance of the considered formulations. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

In the present contribution we propose an improved mixed least-squares finite element method (LSFEM) and compare it with standard LSFEMs with respect to performance aspects. In detail, we consider an approach for Newtonian fluid flow, which is described by the incompressible Navier-Stokes equations. The basis for the associated symmetric minimization problem is a reduced stress-velocity (s-v) two-field approach, see e.g. CAI ET AL. [1] and SCHWARZ & SCHRÖDER [2]. The main idea for the proposed formulation is to add an additional equation, which yields an overconstrained first-order system. This approach does not introduce additional unknowns, so the advantage of two variables (stresses and velocities) remains. Finally, we present a numerical example in order to show the capability of the proposed formulation. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]