We are interested to solve efficiently the steady Stokes equation in a typical 2D domain of gas channels of the hydrogen Fuel Cells, composed of several long straight rectangular sections and of several bends corners. Thus, we propose a 0D-2D Stokes coupled model: velocity and pressure are computed analytically (by asymptotic analysis) in the rectangular sections and numerically (by Finite Elements) in the bends, with appropriate interface conditions. The hurdle to guarantee accuracy and to speed up the computations originates from two sources of error : the choice of the appropriate interface position and the choice of an optimal mesh refinement in the bends. We control these errors building an a posteriori error estimator proved to be reliable and guaranteed (it gives upper bound for the error with constant equal to one) and efficient (it gives lower bound for the error. We propose an original flux reconstruction using the technique of equilibrated fluxes [Ern and Vohralik, 2015] in order to quantify not only the error of the numerical discretization in corners but also the error due to the introduction of the interface and the 0D model. A main novelty of this work is the choice to control the error in pressure measured in the H-1 norm instead of the L2 norm, inspired from work of [Wohlmuth and Dobrowolski, 2008]. This new approach allows us to develop an estimator independent of the inverse of beta, where beta is the LBB inf-sup constant, which is (generally unknown and) very small in the studied case of this work where the domain is very stretched, so that sharp estimates are proved. A numerical validation of the estimator and an adaptive algorithm to choose the interface position and mesh refinement in corners, for a given desired tolerance for the error, complete the talk.