  This work addresses techniques to solve convection-diffusion problems based
on Hermite interpolation. We extend to the case of these equations a Hermite
finite element method providing flux continuity across inter-element
boundaries, shown to be a well-adapted tool for simulating pure diffusion
phenomena (cf. V. Ruas, J. Comput. Appl. Maths., 246 p. 234-242, 2013). We
consider two methods that can be viewed as non trivial improved versions of the
lowest order Raviart-Thomas mixed method, corresponding to its extensions to
convection-diffusion problems proposed by Douglas and Roberts (cf.
Computational and Applied Mathematics, 1, p. 91-103, 1982) . A detailed
convergence study is carried out for one of the methods, and numerical results
illustrate the performance of both of them, as compared to each other and to
the corresponding mixed methods.
