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Advances in Computational Mathematics

, Volume 45, Issue 3, pp 1469–1498 | Cite as

Convergence of an implicit Euler Galerkin scheme for Poisson–Maxwell–Stefan systems

  • Ansgar JüngelEmail author
  • Oliver Leingang
Open Access
Article

Abstract

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 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.

Keywords

Maxwell–Stefan systems Cross diffusion Ionized fluid mixtures Entropy method Finite-element approximation Galerkin method Numerical convergence 

Mathematics Subject Classification (2010)

35K51 35K55 82B35 

Notes

Acknowledgments

Open access funding provided by Austrian Science Fund (FWF).

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Authors and Affiliations

  1. 1.Institute for Analysis and Scientific ComputingVienna University of TechnologyViennaAustria

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