Résumé
A locally superconvergent scheme for the discretization of convective fluxes in a mixed finite-element/finite-volume approach is proposed. This scheme is second-order accurate on the whole unstructured mesh but may enjoy accuracy up to fifth order in cartesian subregions. High-order accuracy is achieved through a particular construction of finite-volume cells and through linear reconstruction of the fluxes at the cell interfaces. The proposed method is applied to the simulation of a laminar boundary layer and of the flow around a square cylinder.