We develop a posteriori upper and lower error bounds for mixed finite-element approximations of a general family of steady, viscous, incompressible quasi-Newtonian flows in a bounded Lipschitz domain Ω \sub Rd ; the family includes degenerate models such as the power law model, as well as non-degenerate ones such as the Carreau model. The unified theoretical framework developed herein yields residualbased a posteriori bounds which measure the error in the approximation of the velocity in the W1,r(Ω) norm and that of the pressure in the L^r'(Ω) norm, 1/r + 1/r' = 1, r 2 (1,∞).

Two-sided a posteriori error bounds for incompressible quasi-Newtonian flows / Berrone, Stefano; Suli, E.. - In: IMA JOURNAL OF NUMERICAL ANALYSIS. - ISSN 0272-4979. - STAMPA. - 28:(2008), pp. 382-421. [10.1093/imanum/drm017]

Two-sided a posteriori error bounds for incompressible quasi-Newtonian flows

BERRONE, Stefano;
2008

Abstract

We develop a posteriori upper and lower error bounds for mixed finite-element approximations of a general family of steady, viscous, incompressible quasi-Newtonian flows in a bounded Lipschitz domain Ω \sub Rd ; the family includes degenerate models such as the power law model, as well as non-degenerate ones such as the Carreau model. The unified theoretical framework developed herein yields residualbased a posteriori bounds which measure the error in the approximation of the velocity in the W1,r(Ω) norm and that of the pressure in the L^r'(Ω) norm, 1/r + 1/r' = 1, r 2 (1,∞).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/1625619
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