A mixed finite element method for a quasi‐Newtonian fluid flow

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.

[1]  P. Ming,et al.  Dual combined finite element methods for Non-Newtonian flow (II) parameter-dependent problem , 2000 .

[2]  M. Fortin,et al.  Dual hybrid methods for the elasticity and the Stokes problems: a unified approach , 1997 .

[3]  George M. Fix,et al.  HYBRID FINITE ELEMENT METHODS , 1976 .

[4]  Mohamed Farhloul,et al.  On a mixed finite element method for the p-Laplacian , 2000 .

[5]  Philippe G. Ciarlet,et al.  The finite element method for elliptic problems , 2002, Classics in applied mathematics.

[6]  J. Baranger,et al.  Analyse numerique des ecoulements quasi-Newtoniens dont la viscosite obeit a la loi puissance ou la loi de carreau , 1990 .

[7]  Jacques Baranger,et al.  Numerical analysis of quasi-Newtonian flow obeying the power low or the Carreau flow , 1990 .

[8]  Jacques Baranger,et al.  Numerical analysis of a three-fields model for a quasi-Newtonian flow , 1993 .

[9]  Wenbin Liu,et al.  Finite element error analysis of a quasi-Newtonian flow obeying the Carreau or power law , 1993 .

[10]  C. E. Vulliamy.  82. A Note on Proto-Neolithic Flint Implements from the Chiltern Hills. , 1927 .

[11]  Abimael F. D. Loula,et al.  Finite element analysis of nonlinear creeping flows , 1990 .

[12]  L. D. Marini,et al.  Two families of mixed finite elements for second order elliptic problems , 1985 .

[13]  W. B. Liu,et al.  Quasi-norm Error Bounds for the Nite Element Approximation of a Non-newtonian Ow , 1994 .

[14]  Vivette Girault,et al.  Finite Element Methods for Navier-Stokes Equations - Theory and Algorithms , 1986, Springer Series in Computational Mathematics.

[15]  G. Galdi.  An Introduction to the Mathematical Theory of the Navier-Stokes Equations : Volume I: Linearised Steady Problems , 1994 .

[16]  Mohamed Farhloul,et al.  A mixed finite element method for a Ladyzhenskaya model , 2002 .

[17]  H. Manouzi,et al.  Mixed finite element analysis of a non‐linear three‐fields Stokes model , 2001 .

[18]  P. Raviart,et al.  A mixed finite element method for 2-nd order elliptic problems , 1977 .

[19]  J. Nédélec.  Mixed finite elements in ℝ3 , 1980 .

[20]  D. Sandri,et al.  Sur l'approximation numérique des écoulements quasi-Newtoniens dont la viscosité suit la loi puissance ou la loi de carreau , 1993 .