CONNECTION BETWEEN FINITE-VOLUME AND MIXED FINITE-ELEMENT METHODS

For the model problem with Laplacian operates we show how to produce c ell-centered finite volume schemes, starting from the mired dual formu lation discretized with the Raviart-Thomas element of lowest order. Th e method is bared on the use of an appropriate integration formula (ma ss lumping) allowing an explicit elimination of the vector variables. The analysis of the finite volume scheme (wellposed-ness and error bou nds) is directly deduced from classical results of mixed finite elemen t theory which is the main interest of the method. We emphasize existe nce and properties of the diagonalizing integration formulas, speciall y in the case of N-dimensional simplicial elements.