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A mixed finite element method for a quasi‐Newtonian fluid flow
Author(s) -
Farhloul M.,
Zine A. M.
Publication year - 2004
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20012
Subject(s) - uniqueness , mixed finite element method , finite element method , conservation law , mathematics , newtonian fluid , non newtonian fluid , extended finite element method , conservation of mass , flow (mathematics) , partial differential equation , mathematical analysis , smoothed finite element method , cauchy stress tensor , finite volume method , physics , geometry , mechanics , boundary knot method , boundary element method , thermodynamics
Abstract We propose a mixed formulation for quasi‐Newtonian fluid flow obeying the power law where the stress tensor is introduced as a new variable. Based on such a formulation, a mixed finite element is constructed and analyzed. This finite element method possesses local (i.e., at element level) conservation properties (conservation of the momentum and the mass) as in the finite volume methods. We give existence and uniqueness results for the continuous problem and its approximation and we prove error bounds. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004.