Augmented saddle-point formulation of the steady-state Stefan–Maxwell diffusion problem

Abstract We investigate structure-preserving finite element discretizations of the steady-state Stefan–Maxwell diffusion problem, which governs mass transport within a phase consisting multiple species. An approach inspired by augmented Lagrangian methods allows us to construct symmetric positive definite Onsager matrix, in turn leads an effective numerical algorithm. prove inf-sup conditions for continuous and discrete linearized systems obtain error estimates arbitrary number The discretization preserves thermodynamically fundamental Gibbs–Duhem equation machine precision independent mesh size. results are illustrated with examples, including application modelling oxygen, carbon dioxide, water vapour nitrogen lungs.