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

## TL;DR

This paper compares four finite volume schemes for an unipolar degenerated drift-diffusion model, analyzing their stability, convergence, and numerical performance to identify effective computational approaches.

## Contribution

The paper introduces and compares four novel finite volume schemes for a degenerated drift-diffusion system, providing stability, existence, and convergence analyses.

## Key findings

- Two schemes proven to converge with respect to discretization parameters
- Numerical experiments illustrate differences in scheme behavior
- Stability and existence results established for all schemes

## Abstract

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 $h(c)=\log \frac{c}{1-c}$. 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.