A numerical analysis focused comparison of several Finite Volume schemes for an Unipolar Degenerated Drift-Diffusion Model
Cl\'ement Canc\`es, Claire Chainais-Hillairet, J\"urgen Fuhrmann, and, Beno\^it Gaudeul
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.
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 and the chemical potential is . 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.
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