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• W2018305879 abstract "A convergence analysis is given for the Scharfetter–Gummel discretization of proto-type one-dimensional continuity equations as arise in the drift-diffusion system modeling semiconductors. These are linear, second-order, boundary-value problems whose coefficient functions are $O(1)$ but can have derivatives that are $O({1 mathord{left/ {vphantom {1 lambda }} right. kern-nulldelimiterspace} lambda })$, for a small positive parameter $lambda $. For such problems, discretizations “of Scharfetter–Gummel type” are proved to be first-order accurate on general meshes uniformly in $lambda $ in a strong global sense. These results improve upon previous analyses, where discrete convergence of $O(h + lambda |ln lambda |)$ was believed to be the best possible." @default.
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• W2018305879 date "1993-06-01" @default.
• W2018305879 modified "2023-09-25" @default.
• W2018305879 title "On the Uniform Convergence of the Scharfetter–Gummel Discretization in One Dimension" @default.
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• W2018305879 doi "https://doi.org/10.1137/0730037" @default.
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