C. Chainais-Hillairet, M. Gisclon, A. Jüngel:
"A Finite-Volume Scheme for the Multidimensional Quantum Drift-Diffusion Model for Semiconductors";
Numerical methods for partial differential equations, 27 (2011), 6; S. 1483 - 1510.

Kurzfassung deutsch:
Siehe englisches Abstract.

Kurzfassung englisch:
A finite-volume scheme for the stationary unipolar quantum drift-diffusion equations for semiconductors in
several space dimensions is analyzed. The model consists of a fourth-order elliptic equation for the electron
density, coupled to the Poisson equation for the electrostatic potential, with mixed Dirichlet-Neumann
boundary conditions. The numerical scheme is based on a Scharfetter-Gummel type reformulation of the
equations. The existence of a sequence of solutions to the discrete problem and its numerical convergence to
a solution to the continuous model are shown. Moreover, some numerical examples in two space dimensions
are presented.

Density-gradient model; finite-volume method; numerical convergence

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