Filters

2019 - 201912020 - 20222

More filters

20223
Reset filters

Settings

Author: Gaudeul, Benoît × Type: Text ×

Search Results

Now showing 1 - 3 of 3
  • Thumbnail Image
    Item
    Entropy and convergence analysis for two finite volume schemes for a Nernst–Planck–Poisson system with ion volume constraints
    (Berlin ; Heidelberg : Springer, 2022) 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.
  • Thumbnail Image
    Item
    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.
  • Thumbnail Image
    Item
    A numerical analysis focused comparison of several finite volume schemes for an unipolar degenerated drift-diffusion model
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Cancès, Clément; Chainais-Hillairet, Claire; Fuhrmann, Jürgen; Gaudeul, Benoît
    In this paper, we consider an unipolar degenerated drift-diffusion system where the relation between the concentration of the charged species c and the chemical potential h is h(c) = log c/1-c. We design four different finite volume schemes based on four different formulations of the fluxes. We provide a stability analysis and existence results for the four schemes. The convergence proof with respect to the discretization parameters is established for two of them. Numerical experiments illustrate the behaviour of the different schemes.