×

zbMATH — the first resource for mathematics

Finite element error analysis of a quasi-Newtonian flow obeying the Carreau or power law. (English) Zbl 0796.76049
Summary: We consider the finite element approximation of a quasi-Newtonian flow, where the viscosity obeys the Carreau or power law. For sufficiently regular solutions, we prove energy type error bounds for the velocity and pressure. These bounds improve on results existing in the literature.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76A05 Non-Newtonian fluids
PDF BibTeX XML Cite
Full Text: DOI EuDML
References:
[1] Amrouche, C., Girault, V. (1990): Propri?t?s fonctionnelles d’op?rateurs. Application au probl?me de Stokes en dimension quelconque. Publications du Labratoire d’Analyse Num?rique, n. 90025, Universit? Pierre et Marie Curie
[2] Baranger, J., Najib, K. (1990): Analyse num?rique des ?coulements quasi-Newtoniens dont la viscosit? ob?it ? la loi puissance ou la loi de Carreau. Numer. Math.58, 35-49 · Zbl 0702.76007 · doi:10.1007/BF01385609
[3] Barrett, J.W., Liu, W.B. (1991): Finite element approximation of thep-Laplacian. Submitted for publication
[4] Bernardi, C., Raugel, G. (1985): Analysis of some finite elements for the Stokes problem. Math. Comput.44, 71-79 · Zbl 0563.65075 · doi:10.1090/S0025-5718-1985-0771031-7
[5] Chow, S.-S. (1989): Finite element error estimates for non-linear elliptic equations of monotone type. Numer. Math.54, 373-393 · Zbl 0643.65058 · doi:10.1007/BF01396320
[6] Ciarlet, P.G. (1978): The finite element method for elliptic problems. North Holland, Amsterdam · Zbl 0383.65058
[7] Fortin, M. (1981): Old and new finite elements for incompressible flows. Int. J. Numer. Meth. Fluids1, 347-364 · Zbl 0467.76030 · doi:10.1002/fld.1650010406
[8] Girault, V., Raviart, P.-A. (1986): Finite element methods for Navier-Stokes equations. Springer, Berlin Heidelberg New York · Zbl 0585.65077
[9] Liu, W.B., Barrett, J.W. (1991): Finite element approximation of some degenerate monotone quasilinear elliptic systems. Submitted for publication · Zbl 0846.65064
[10] Mosolov, P.P., Mjasnikov, V.P. (1971): A proof of Korn’s inequality. Soviet Math. Dokl.12, 1618-1622 · Zbl 0248.52011
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.