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In this paper, we consider an unipolar degenerated drift-diffusion systemwhere the relation between the concentration of the charged species $c$ and thechemical potential $h$ is $h(c)=\log \frac{c}{1-c}$. We design four differentfinite volume schemes based on four different formulations of the fluxes. Weprovide a stability analysis and existence results for the four schemes. Theconvergence proof with respect to the discretization parameters is establishedfor two of them. Numerical experiments illustrate the behaviour of thedifferent schemes.

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