A numerical-analysis-focused comparison of several finite volume schemes for a unipolar degenerate drift-diffusion model

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 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.

Automated summary

In this paper, a unipolar degenerate drift-diffusion system with a specific relation between concentration of charged species c and chemical potential h is considered. Four different finite volume schemes based on different formulations of fluxes are designed, with stability analysis and existence results provided for all four schemes. Convergence proof with respect to discretization parameters is established for two of the schemes, and numerical experiments illustrate the behavior of the schemes.