In this paper 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 |$h(c)=\log \frac{c}{1-c}$|⁠. 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.

中文翻译：

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以数值分析为重点的单极性简并漂移扩散模型的几种有限体积方案比较

在本文中，我们考虑单极性简并漂移扩散系统，其中带电物质的浓度之间的关系| $ c $ |。和化学势| $ h $ | 是| $ h（c）= \ log \ frac {c} {1-c} $ |⁠。我们基于四种不同的通量公式设计了四种不同的有限体积方案。我们提供了四种方案的稳定性分析和存在性结果。对于其中两个，建立了关于离散化参数的收敛性证明。数值实验说明了不同方案的行为。