English

A numerical analysis focused comparison of several Finite Volume schemes for an Unipolar Degenerated Drift-Diffusion Model

Numerical Analysis 2019-07-29 v2 Numerical Analysis Analysis of PDEs Computational Physics

Abstract

In this paper, we consider an unipolar degenerated drift-diffusion system where the relation between the concentration of the charged species cc and the chemical potential hh is h(c)=logc1ch(c)=\log \frac{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.

Keywords

Cite

@article{arxiv.1907.11126,
  title  = {A numerical analysis focused comparison of several Finite Volume schemes for an Unipolar Degenerated Drift-Diffusion Model},
  author = {Clément Cancès and Claire Chainais-Hillairet and Jürgen Fuhrmann and Benoît Gaudeul},
  journal= {arXiv preprint arXiv:1907.11126},
  year   = {2019}
}