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Least‐squares finite element methods for the Navier‐Stokes equations for generalized Newtonian fluids
Author(s) -
Serdas Serdar,
Schwarz Alexander,
Schröder Jörg,
Turek Stefan,
Ouazzi Abderrahim,
Nickaeen Masoud
Publication year - 2014
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201410299
Subject(s) - finite element method , newtonian fluid , compressibility , non newtonian fluid , mathematics , generalized newtonian fluid , navier–stokes equations , constitutive equation , incompressible flow , mathematical analysis , order (exchange) , least squares function approximation , flow (mathematics) , physics , classical mechanics , mechanics , geometry , viscosity , thermodynamics , shear rate , statistics , estimator , finance , economics
In this contribution we present the least‐squares finite element method (LSFEM) for the incompressible Navier‐Stokes equations. In detail, we consider a non‐Newtonian fluid flow, which is described by a power‐law model, see [1]. The second‐order problem is reformulated by introducing a first‐order div‐grad system consisting of the equilibrium condition, the incompressibility condition and the constitutive equation, which are written in residual forms, see [2]. Here, higher‐order finite elements which are an important aspect regarding accuracy for the present formulation are investigated. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)