Least‐squares finite element methods for the Navier‐Stokes equations for generalized Newtonian fluids | Zendy

Serdas Serdar | Zendy; Schwarz Alexander | Zendy; Schröder Jörg | Zendy; Turek Stefan | Zendy; Ouazzi Abderrahim | Zendy; Nickaeen Masoud | Zendy

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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)

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