  A fully discrete Galerkin scheme for a thermodynamically consistent transient
Max-well-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 boundedness, 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.
