An artificial boundary condition method, derived in terms of infinite Fourier
series, is applied to solve a class of quasi-Newtonian Stokes flows. Based on the natural
boundary reduction involving an artificial condition on the artificial boundary, the coupled
variational problem and its numerical solution are obtained. The unique solvability
of the continuous and discrete formulations are discussed, and the error analysis for the
problem is also considered. Finally, an a posteriori error estimate for the corresponding
problem is provided.