Abstract
We consider a unipolar degenerate drift-diffusion system where the relation between the concentration of the charged species c and the chemical potential h is \(h(c)=\log \frac{c}{1-c}\). For four different finite volume schemes based on four different formulations of the fluxes of the problem, we discuss stability and existence results. For two of them, we report a convergence proof. Numerical experiments illustrate the behaviour of the different schemes.
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Cancès, C., Hillairet, C.C., Fuhrmann, J., Gaudeul, B. (2020). On Four Numerical Schemes for a Unipolar Degenerate Drift-Diffusion Model. In: Klöfkorn, R., Keilegavlen, E., Radu, F.A., Fuhrmann, J. (eds) Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples. FVCA 2020. Springer Proceedings in Mathematics & Statistics, vol 323. Springer, Cham. https://doi.org/10.1007/978-3-030-43651-3_13
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DOI: https://doi.org/10.1007/978-3-030-43651-3_13
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