A discontinuous Galerkin method for coupled elasto-diffusion

A discontinuous Galerkin (DG) method will be discussed for the coupling of elasticity and diffusion. The motivation comes from an elementary analysis of the simplest, coupled elasto-diffusion problem. This analysis exposes a higher-order continuity requirement on the displacement field. After an outline of this analysis, we proceed to a formulation of the coupled problem in the framework of DG methods. Specifically, we present a class of DG methods that account for inter-element discontinuities in a variationally-consistent manner. This DG formulation is the basis for a finite element implementation that retains consistency with interpolations, the higher-order continuity conditions notwithstanding. An error analysis of the DG formulation has been developed and will be presented. In conclusion a comparison of numerical results with the standard Galerkin finite element formulation and a mixed formulation will be carried out.