Abstract
Received September , 2011Received in revised form November, 2011Abstract — A new technique for the implementation of cell-centered finite volume schemesis proposed. It is based on an equivalence between these schemes and the non-conformingCrouzeix-Raviart finite element approximation. Though the implementation somewhat increasesthe number of unknowns, it brings two significant advantages that make it attractive. On the onehand the resulting formulation is well-defined on general unstructured meshes, with no restric-tion on (or ad-hoc treatment of) obtuse angles. On the other hand, it automatically provides avery effective, asymptotically exact, error estimator. An adaptive finite volume method, basedon this estimator, is proposed and tested. It turns out to be remarkable for its exactness, even incoarse meshes.Keywords: Finite Volume, Mixed Finite Element, Nonconforming Finite Element AdaptiveMethod, Error Estimator.
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