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This work is motivated by the need of efficient numerical simulations of gasflows in the serpentine channels used in proton-exchange membrane fuel cells.In particular, we consider the Poisson problem in a 2D domain composed ofseveral long straight rectangular sections and of several bends corners. Inorder to speed up the resolution, we propose a 0D model in the rectangularparts of the channel and a Finite Element resolution in the bends. To find agood compromise between precision and time consuming, the challenge is double:how to choose a suitable position of the interface between the 0D and the 2Dmodels and how to control the discretization error in the bends. We shallpresent an \textit{a posteriori} error estimator based on an equilibrated fluxreconstruction in the subdomains where the Finite Element method is applied.The estimates give a global upper bound on the error measured in the energynorm of the difference between the exact and approximate solutions on the wholedomain. They are guaranteed, meaning that they feature no undeterminedconstants. (global) Lower bounds for the error are also derived. An adaptivealgorithm is proposed to use smartly the estimator for aforementioned doublechallenge. A numerical validation of the estimator and the algorithm completesthe work. \end{abstract}

An a posteriori error estimate for a 0D/2D coupled model