Analysis and mixed-primal finite element discretisations for stress-assisted diffusion problems

Journal article

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 exerted in the solid. 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 schemes 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.

Authors: Gatica, G; Gomez, B; Ruiz Baier, R

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Elsevier
• Journal: Computer Methods in Applied Mechanics and Engineering
• Volume: 337
• Pages: 411-438
• Publication date: 2018-04-06
• Acceptance date: 2018-03-26
• DOI: 10.1016/j.cma.2018.03.043
• ISSN: 0045-7825
• Keywords: mixed-primal formulation; a priori error bounds; linear elasticity; fixed-point theory; stress-assisted diffusion; finite element methods