On four numerical schemes for a unipolar degenerate drift-diffusion model
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 $h(c) = log(c/(1−c))$. 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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