We develop the a posteriori error analysis of finite element approximations of implicit power-law-like models for viscous incompressible fluids. The Cauchy stress and the symmetric part of the velocity gradient in the class of models under consideration are related by a, possibly multi--valued, maximal monotone r-graph, with 2d/d+1<r<∞. We establish upper and lower bounds on the finite element residual, as well as the local stability of the error bound. We then consider an adaptive finite

more »

... t approximation of the problem, and, under suitable assumptions, we show the weak convergence of the adaptive algorithm to a weak solution of the boundary-value problem. The argument is based on a variety of weak compactness techniques, including Chacon's biting lemma and a finite element counterpart of the Acerbi--Fusco Lipschitz truncation of Sobolev functions, introduced by L. Diening, C. Kreuzer and E. Süli [Finite element approximation of steady flows of incompressible fluids with implicit power-law-like rheology. SIAM J. Numer. Anal., 51(2), 984--1015].