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

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) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Proceedings in Applied Mathematics & Mechanics Wiley

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

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Publisher
Wiley Subscription Services, Inc., A Wiley Company
Copyright
Copyright © 2017 Wiley Subscription Services
ISSN
1617-7061
eISSN
1617-7061
D.O.I.
10.1002/pamm.201710285
Publisher site
See Article on Publisher Site

Abstract

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)

Journal

Proceedings in Applied Mathematics & MechanicsWiley

Published: Jan 1, 2017

References

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