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Investigation of stress‐velocity LSFEMs for the incompressible Navier‐Stokes equations
Author(s) -
Nisters Carina,
Schwarz Alexander,
Schröder Jörg
Publication year - 2017
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201710285
Subject(s) - mathematics , compressibility , finite element method , pressure correction method , mathematical analysis , least squares function approximation , matrix (chemical analysis) , navier–stokes equations , stress (linguistics) , reynolds number , boundary value problem , mechanics , physics , materials science , thermodynamics , linguistics , statistics , philosophy , estimator , turbulence , composite material
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)