  This work is motivated by the need of efficient numerical simulations of gas
flows in the serpentine channels used in proton-exchange membrane fuel cells.
In particular, we consider the Poisson problem in a 2D domain composed of
several long straight rectangular sections and of several bends corners. In
order to speed up the resolution, we propose a 0D model in the rectangular
parts of the channel and a Finite Element resolution in the bends. To find a
good compromise between precision and time consuming, the challenge is double:
how to choose a suitable position of the interface between the 0D and the 2D
models and how to control the discretization error in the bends. We shall
present an \textit{a posteriori} error estimator based on an equilibrated flux
reconstruction in the subdomains where the Finite Element method is applied.
The estimates give a global upper bound on the error measured in the energy
norm of the difference between the exact and approximate solutions on the whole
domain. They are guaranteed, meaning that they feature no undetermined
constants. (global) Lower bounds for the error are also derived. An adaptive
algorithm is proposed to use smartly the estimator for aforementioned double
challenge. A numerical validation of the estimator and the algorithm completes
the work. \end{abstract}
