Adaptive Finite Volume Scheme for Elliptic Problems
نویسندگان
چکیده
A new technique for the implementation of cell-centered nite volume schemes is proposed. It is based on a recently found equivalence between these schemes and the non-conforming Crouzeix-Raviart nite element approximation. Though the implementation somewhat increases the number of unknowns, it brings two signiicant advantages that make it attractive. On the one hand the resulting formulation is well-deened on general unstructured meshes, with no restriction on (or ad-hoc treatment of) obtuse angles. On the other hand, it automatically provides a very eeective, asymptotically exact, error estimator. An adaptive nite volume method, based on this estimator, is proposed and tested. It turns out to be remarkable for its exactness, even in coarse meshes.
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