A POSTERIORI ERROR ESTIMATION FOR A DUAL MIXED
FINITE ELEMENT METHOD FOR QUASI-NEWTONIAN
FLOWS WHOSE VISCOSITY OBEYS A POWER LAW OR
CARREAU LAW
Mohamed Farhloul1, Abdelmalek Zine2
1Département de Mathématiques et de Statistique
Université de Moncton
Moncton, N.B., E1A 3E9, CANADA
2Département de Mathématiques et Informatique
Université de Lyon
Institut Camille Jordan, CNRS-UMR5208
Ecole Centrale de Lyon, 36 av. Guy de Collongue
69134 Ecully Cedex, FRANCE

Abstract

A dual mixed finite element method, for quasi-Newtonian fluid flow obeying the power law or the Carreau law, is constructed and analyzed in Farhloul-Zine [13]. This mixed formulation possesses good local (i.e., at element level) conservation properties (conservation of the momentum and the mass) as in the finite volume methods. In Farhloul-Zine [12], we developed an a posteriori error analysis for a non-Newtonian fluid flow problems. The analysis is based on the fact that the equation describing the extra-stress tensor in terms of the rate of strain tensor is invertible and may give the rate of strain tensor as a function of the stress tensor. To free ourselves from this constraint of inversion of laws, and as a generalization of the obtained results in [12], we propose in this work an a posteriori error analysis to this mixed formulation.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 30
Issue: 5
Year: 2017

DOI: 10.12732/ijam.v30i5.1

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