Mixed finite element analysis of a non-linear three-fields Stokes model

Manouzi, Hassan; Farhloul, Mohamed

doi:10.1093/imanum/21.1.143

Cited by 25 publications

(31 citation statements)

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“…The work in this paper extends the investigates of [4,23,15]. In [4] Baranger, Najib, and Sandri provided an analysis for the existence and uniqueness of the modeling equations in appropriate Sobolev spaces and gave an error analysis of a finite element approximation method applied to the primitive variables (σ, p, u).…”

Section: Ladyzhenskaya Law[21]mentioning

confidence: 72%

“…In [4] Baranger, Najib, and Sandri provided an analysis for the existence and uniqueness of the modeling equations in appropriate Sobolev spaces and gave an error analysis of a finite element approximation method applied to the primitive variables (σ, p, u). Manouzi and Farhloul in [23] reformulated the modeling equations into a saddle point problem and used a mixed formulation to study the existence and uniqueness of the solution, again in appropriate Sobolev spaces. An error analysis for the finite element approximation was also given.…”

Section: Ladyzhenskaya Law[21]mentioning

confidence: 99%

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A dual-mixed approximation method for a three-field model of a nonlinear generalized Stokes problem

Ervin

Howell

Stanculescu

2008

Computer Methods in Applied Mechanics and Engineering

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Abstract. In this work a dual-mixed approximation of a nonlinear generalized Stokes problem is studied. The problem is analyzed in Sobolev spaces which arise naturally in the problem formulation. Existence and uniqueness results are given and error estimates are derived. It is shown that both lowest-order and higher-order mixed finite elements are suitable for the approximation method. Numerical experiments that support the theoretical results are presented.

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Section: Ladyzhenskaya Law[21]mentioning

confidence: 72%

Section: Ladyzhenskaya Law[21]mentioning

confidence: 99%

A dual-mixed approximation method for a three-field model of a nonlinear generalized Stokes problem

Ervin

Howell

Stanculescu

2008

Computer Methods in Applied Mechanics and Engineering

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“…Other constitutive equations having a similar form to the power law model include [3,13,14]: Ladyzhenskaya Law [12]: 8) used in modeling fluids with large stresses, Carreau Law :…”

Section: Problem Specificationmentioning

confidence: 99%

“…The numerical approximation of the quasi-Newtonian Stokes flow problem, with homogeneous boundary conditions has been previously studied in several papers [2,5,7,13,16]. This paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

Numerical Approximation of a Quasi-Newtonian Stokes Flow Problem with Defective Boundary Conditions

Ervin¹,

Lee²

2007

SIAM J. Numer. Anal.

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Abstract. In this article we study the numerical approximation of a quasi-Newtonian Stokes flow problem where only the flow rates are specified at the inflow and outflow boundaries. A variational formulation of the problem, using Lagrange multipliers to enforce the stated flow rates, is given. Existence and uniqueness of the solution to the continuous, and discrete, variational formulations is shown. An error analysis for the numerical approximation is also given. Numerical computations are included which demonstrate the approximation scheme studied.

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“…Among these works, there may be mentioned Manouzi and Farhloul [18], Farhloul and Zine [10], Gatica et al [15,16] and Ervin et al [9]. The major drawback of formulations using the gradient lies in the fact that we can not deal with natural boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

{\em A POSTERIORI} ERROR ESTIMATION FOR A DUAL MIXED FINITE ELEMENT METHOD FOR QUASI--NEWTONIAN FLOWS WHOSE VISCOSITY OBEYS A POWER LAW OR CARREAU LAW

Farhloul¹,

Zine²

2017

Int. J. of Appl. Math.

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A dual mixed finite element method, for quasi-Newtonian fluid flow obeying the power law or the Carreau law, is constructed and analyzed in . 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.

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Mixed finite element analysis of a non-linear three-fields Stokes model

Cited by 25 publications

References 0 publications

A dual-mixed approximation method for a three-field model of a nonlinear generalized Stokes problem

A dual-mixed approximation method for a three-field model of a nonlinear generalized Stokes problem

Numerical Approximation of a Quasi-Newtonian Stokes Flow Problem with Defective Boundary Conditions

{\em A POSTERIORI} ERROR ESTIMATION FOR A DUAL MIXED FINITE ELEMENT METHOD FOR QUASI--NEWTONIAN FLOWS WHOSE VISCOSITY OBEYS A POWER LAW OR CARREAU LAW

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