Investigation of stress-velocity LSFEMs for the incompressible Navier-Stokes equations

In this contribution three mixed least-squares finite element methods (LSFEMs) for the incompressible Navier-Stokes equations are investigated with respect to accuracy and efficiency. The well-known stress-velocity-pressure formulation is the basis for two further div-grad least-squares formulations in terms of stresses and velocities (SV). Advantage of the SV formulations is a system with a smaller matrix size due to a reduction of the degrees of freedom. The least-squares finite element formulations, which are investigated in this contribution, base on the incompressible stationary Navier-Stokes equations. The first formulation under consideration is the stress-velocity-pressure formulation according to 1]. Secondly, an extended stress-velocity formulation with an additional residual is derived based on the findings in 1] and 5]. The third formulation is a pressure reduced stress-velocity formulation based on a condensation scheme. Therefore, the pressure is interpolated discontinuously, and eliminated on the discrete level without the need for any matrix inverting. The modified lid-driven cavity boundary value problem, is investigated for the Reynolds number Re = 1000 for all three formulations. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)