Chainais-Hillairet, Claire; Peng, Yue-Jun Convergence of a finite-volume scheme for the drift-diffusion equations in 1D. (English) Zbl 1018.65109 IMA J. Numer. Anal. 23, No. 1, 81-108 (2003). 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. Reviewer: Ruxandra Stavre (Bucureşti) Cited in 12 Documents 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 Keywords:finite volume scheme; numerical examples; semiconductor model; degenerate parabolic equations; nonlinear drift-diffusion equations; convergence PDFBibTeX XMLCite \textit{C. Chainais-Hillairet} and \textit{Y.-J. Peng}, IMA J. Numer. Anal. 23, No. 1, 81--108 (2003; Zbl 1018.65109) Full Text: DOI