FINITE-VOLUME BOX SCHEMES ON TRIANGULAR MESHES

We introduce a finite volume box scheme for equations in divergence fo rm - div (phi(u)) = f, which is a generalization of the box scheme of Keller As in Keller's scheme, affine approximations both of the unknow n and of the flux yi are used in each cell. Although the scheme is not variationnal, finite element spaces are used. We emphasize the case w here the approximation spaces are the nonconforming P-1-space of Crouz eix-Raviart for the primary unknown u, and the divergence conforming s pace of Raviart-Thomas for the flux VI We prove art error estimate in the discrete energy seminorm for the Poisson problem. Finally, some nu merical results and implementation details are given, proving that the scheme is effectively of second order (C) Elsevier Paris.