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

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 ; 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 residual-based 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 Lr′(Ω) norm, 1/r + 1/r′ = 1, r ∈ (1, ∞).