Mixed hybrid finite volume analysis of a 1D diffusion model

Abstract

We present in this paper a numerical method using basic ideas of mixed hybrid finite element and finite volume methods. It is the reason why we call it mixed hybrid finite volume method. Given a one-dimensional diffusion problem we develop the main aspects of this numerical approach. We show the connection with the classical mixed hybrid finite element method. We also show that mixed hybrid finite volume is an extension of the classical finite volume method at least for diffusion problems. We establish some error estimates with respect to a discrete version of H10norm for the potential and L2 in ||·||_infinity norms for the velocity