Abstract
A fully discrete implicit Euler upwind finite volume element method is derived and studied for one-dimensional semiconductor device. Upwind scheme is introduced to deal with the convection-dominated diffusion equations in the semiconductor model. With different time steps for the electrostatic potential and the other unknown quantities, the computational procedure of the method is obtained. The local mass conservation laws are preserved under the framework of the upwind finite volume element schemes. A first-order accuracy in the L 2-norm is proved. Numerical experiments are given to validate the usefulness and efficiency of the method.
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This work is supported in part by Shandong Province Natural Science Foundation under Grant No. ZR2010AQ010 and a Project of Shandong Province Higher Educational Science and Technology Program under Grant Nos. J11LA09 and J10LA01.
This paper was recommended for publication by Editor Ningning YAN.
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Chen, C., Liu, W. & Lu, D. Upwind finite volume element methods for one-dimensional semiconductor device. J Syst Sci Complex 24, 1007–1019 (2011). https://doi.org/10.1007/s11424-011-9021-4
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DOI: https://doi.org/10.1007/s11424-011-9021-4