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

In this paper, we consider an unipolar degenerated 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.

Keywords

Finite volume methods, drift-diffusion equations

URI

https://oa.tib.eu/renate/handle/123456789/9204
https://doi.org/10.34657/8242

Citation

Cancès, C., Chainais-Hillairet, C., Fuhrmann, J., & Gaudeul, B. (2019). A numerical analysis focused comparison of several finite volume schemes for an unipolar degenerated drift-diffusion model (Vol. 2620). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik. https://doi.org//10.20347/WIAS.PREPRINT.2620

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Mathematik

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