Residual a posteriori error estimator for a three-field model of a non-linear generalized Stokes problem

In this article we propose and analyze an a posteriori error estimator for a three-field model of a generalized Stokes problem. The components of the a posteriori error estimator are defined via a non-linear projection of the residues of the variational equations. Both upper and lower bounds for the approximation error are derived in terms of the components of the a posteriori error estimator. The non-linear projections do not need to be explicitly computed to construct the a posteriori error estimates.