WIAS Preprint No. 2811, (2021)

Entropy and convergence analysis for two finite volume schemes for a Nernst--Planck--Poisson system with ion volume constraints


Authors

  • Gaudeul, Benoît
  • Fuhrmann, Jürgen
    ORCID: 0000-0003-4432-2434

2020 Mathematics Subject Classification

  • 65N08 78A57 35Q81

Keywords

  • finite volume methods, drift-diffusion equations, generalized Nernst--Planck--Poisson system, finite size effects

DOI

10.20347/WIAS.PREPRINT.2811

Abstract

In this paper, we consider a drift-diffusion system with cross-coupling through the chemical potentials comprising a model for the motion of finite size ions in liquid electrolytes. The drift term is due to the self-consistent electric field maintained by the ions and described by a Poisson equation. We design two finite volume schemes based on different formulations of the fluxes. We also provide a stability analysis of these schemes and an existence result for the corresponding discrete solutions. A convergence proof is proposed for non-degenerate solutions. Numerical experiments show the behavior of these schemes.

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