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

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