On a coupled finite element-finite volume method for convection-diffusion problems

In this paper we present and analyse a coupled finite element-finite volume method for the numerical approximation of singularly perturbed convection-diffusion problems. The idea is to couple a discretization for the convective term, based on the finite volume (node-centred) method, and a standard continuous finite element approximation of the diffusive term. Such a method preserves conservation, fulfils consistency and enhances stability.