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 and the chemical potential is . 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}
}