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A. Jüngel, O. Leingang:
"Convergence of an implicit Euler Galerkin scheme for Poisson-Maxwell-Stefan systems";
in: "ASC Report 22/2018", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2018, ISBN: 978-3-902627-11-7, 1 - 28.

A fully discrete Galerkin scheme for a thermodynamically consistent transient Maxwell-Stefan system for the mass particle densities, coupled to the Poisson equation for the electric potential, is investigated. The system models the diffusive dynamics of an isothermal ionized fluid mixture with vanishing barycentric velocity. The equations are studied in a bounded domain, and different molar masses are allowed. The Galerkin scheme preserves the total mass, the nonnegativity of the particle densities, their bound-edness, and satisfies the second law of thermodynamics in the sense that the discrete entropy production is nonnegative. The existence of solutions to the Galerkin scheme and the convergence of a subsequence to a solution to the continuous system is proved. Compared to previous works, the novelty consists in the treatment of the drift terms involving the electric field. Numerical experiments show the sensitive dependence of the particle densities and the equilibration rate on the molar masses.

Maxwell-Stefan systems, cross diffusion, ionized fluid mixtures, entropy method, finite-element approximation, Galerkin method, numerical convergence.

http://www.asc.tuwien.ac.at/preprint/2018/asc22x2018.pdf