A Hermite Finite Element Method for Convection-diffusion Equations

This work addresses a technique to solve convection-diffusion problems based on Hermite interpolation. More specifically we extend to the case of these equations a Hermite finite element method providing flux continuity across interelement boundaries, shown to be a well-adapted tool for simulating purely diffusive phenomena [6]. The method can be viewed as a non trivial improved version of the lowest order Raviart-Thomas mixed method [4] and its extension to convection-diffusion problems proposed by Douglas and Roberts [2]. Convergence results are proven to hold, and comparative numerical results illustrate the good performance of the new method.