By Jean Laurent

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To prove the convergence of the numerical method, it remains to pass to the limit in the scheme and by this way prove that the limit of the sequence of approximate solutions is a weak solution to (Pρ ). It can be done as in [11], but dealing with the Scharfetter-Gummel fluxes as in [3]. 4 Some Numerical Experiments We illustrate now the stability of the fully implicit Scharfetter-Gummel scheme for all nonnegative values of the rescaled Debye length ρ. Therefore, we consider a one dimensional test case on π = (0, 1).

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