Connection between finite volume and mixed finite element methods

Abstract

For the model problem with Laplacian operator, we show how to produce cell-centered finite volume schemes, starting from the mixed dual formulation discretized with the Raviart-Thomas element of lowest order. The method is based on the use of an appropriate integration formula (mass lumping) allowing an explicit elimination of the vector variables. The analysis of the finite volume scheme (wellposed-ness and error bounds) is directly deduced from classical results of mixed finite element theory, which is the main interest of the method. We emphasize existence and properties of the diagonalizing integration formulas, specially in the case of N-dimensional simplicial elements.