Analyse numérique des écoulements quasi-Newtoniens dont la viscosité obéit à la loi puissance ou la loi de Carreau. (Numerical analysis of quasi-Newtonian flow obeying the power low or the Carreau flow). (French) Zbl 0702.76007

Summary: We prove abstract error estimates for the approximation of the velocity and the pressure by a mixed FEM of quasi-Newtonian flows whose viscosity obeys the power law or the Carreau law. These estimates are optimal in some cases. They can be applied to most finite elements used for the solution of Stokes’s problem.


76A05 Non-Newtonian fluids
65N15 Error bounds for boundary value problems involving PDEs
76M10 Finite element methods applied to problems in fluid mechanics
Full Text: DOI EuDML


[1] Baranger, J., Georget, P., Najib, K.: Error estimates for a mixed finite element method for a non Newtonian flow. J. Non-Newtonian Fluid Mech.23, 415-421 (1987) · Zbl 0619.76003
[2] Baranger, J., Najib, K.: Local inf-sup condition and mixed finite element methods for quasi Newtonian flows?Ve Congr?s International sur les m?thodes num?riques de l’ing?nieur-Lausanne. 11-15 Septembre 1989
[3] Bernardi, C., Raugel, G.: Analysis for some finite elements for the Stokes problem. Math. Comput.44, 71-79 (1985) · Zbl 0563.65075
[4] Boland, J., Nicholaides, R.: Stability of finite element under divergence constraints. SIAM J. Numer. Anal.20, 722-731 (1983) · Zbl 0521.76027
[5] Brezzi, F.: On the existence uniqueness and approximation of saddle-point problems arising from Lagrange multipliers. RAIRO, Modelisation Math. Anal. Numer.8, 129-151 (1974) · Zbl 0338.90047
[6] Chow, S.S.: Finite element error estimates for non linear elliptic problems of monotone type-PHD Australian National University 1983
[7] Ciarlet, P.G.: The finite element methods for elliptic problems. North Holland 1978 · Zbl 0383.65058
[8] Clement, P.: Approximation by finite element functions using local regularization. RAIRO Modelisation Math. Anal. Numer.9, 77-84 (1975) · Zbl 0368.65008
[9] Fortin, M.: Old and new finite elements for incompressible flows. Int. J. Numer. Methods Fluids1, 347-364 (1981) · Zbl 0467.76030
[10] Georget, P.: Contribution ? l’?tude des ?quations de Stokes ? viscosit? variable. Th?se Universit? Lyon1, 1985
[11] Girault, V., Raviart, P.A.: Finite element methods for Navier-Stokes Equations. Berlin Heidelberg New York: Springer 1986 · Zbl 0585.65077
[12] Glowinski, R., Marroco, A.: Sur l’approximation par ?l?ments finis d’ordre 1 et la resolution par p?nalisation-dualit? d’une classe de probl?mes de Dirichlet non lin?aires. RAIRO Modelisation Math. Anal. Numer.9, 41-76 (1975) · Zbl 0368.65053
[13] Mjasnikov, V.P., Mosolov, P.P.: A proof of Korn Inequality. Sov. Math.12, 1618-1622 (1971) · Zbl 0248.52011
[14] Najib, K.: Analyse Num?rique de mod?les d’?coulements quasi-newtoniens. Th?se Universit? Lyon1, 1988
[15] Scheurer, B.: Existence et approximation de points selles pour certains probl?mes non lin?aires. RAIRO Modelisation Math. Anal. Numer.11, 369-400 (1977) · Zbl 0371.65025
[16] Tyukhtin, V.B.: Sur la vitesse de convergence des m?thodes d’approximation de la solution des probl?mes variationnels unilat?raux (en russe). Vestn. Leningr. Univ., Math. Mec. Astronom.3, 36-43 (1983)
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