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Convergence of a finite-volume scheme for the drift-diffusion equations in 1D. (English) Zbl 1018.65109

An approximate solution of the one-dimensional nonlinear drift-diffusion equations is constructed, by using a finite volume scheme. The convergence of the scheme is obtained, which yields the global existence of the solutions. It is proved that this result is valid even in the presence of vacuum state. Finally, numerical simulations are performed.

MSC:

65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35K55 Nonlinear parabolic equations
35K65 Degenerate parabolic equations
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