Gabriel N. Gatica, Bryan Gomez-Vargas, Ricardo Ruiz-Baier:
Mixed-primal finite element methods for stress-assisted diffusion problems
We analyse the solvability of a static coupled system of PDEs describing the diffusion of a solute into an elastic material, where the process is affected by the stresses generated in by the solid motion. The problem is formulated in terms of solid stress, rotation tensor, solid displacement, and concentration of the solute. Existence and uniqueness of weak solutions follow from adapting a fixed-point strategy decoupling linear elasticity from a generalised Poisson equation. We then construct mixed-primal and augmented mixed-primal Galerkin discretisations based on adequate finite element spaces, for which we rigorously derive a priori error bounds. The convergence of these methods is confirmed through a set of computational tests in 2D and 3D.