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Subject: generalized Nernst--Planck--Poisson system × WGL Institute: WIAS ×

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    Entropy and convergence analysis for two finite volume schemes for a Nernst--Planck--Poisson system with ion volume constraints
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Gaudeul, Benoît; Fuhrmann, Jürgen
    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.