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Error analysis of the semi-discrete local discontinuous Galerkin method for semiconductor device simulation models

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Abstract

In this paper we continue our effort in Liu-Shu (2004) and Liu-Shu (2007) for developing local discontinuous Galerkin (LDG) finite element methods to discretize moment models in semiconductor device simulations. We consider drift-diffusion (DD) and high-field (HF) models of one-dimensional devices, which involve not only first derivative convection terms but also second derivative diffusion terms, as well as a coupled Poisson potential equation. Error estimates are obtained for both models with smooth solutions. The main technical difficulties in the analysis include the treatment of the inter-element jump terms which arise from the discontinuous nature of the numerical method, the nonlinearity, and the coupling of the models. A simulation is also performed to validate the analysis.

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Authors and Affiliations

  1. School of Mathematics, Shandong University, Jinan, 250100, China

    YunXian Liu

  2. Division of Applied Mathematics, Brown University, Providence, RI, 02912, USA

    Chi-Wang Shu

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  1. YunXian Liu
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  2. Chi-Wang Shu
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Correspondence to YunXian Liu.

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Liu, Y., Shu, CW. Error analysis of the semi-discrete local discontinuous Galerkin method for semiconductor device simulation models. Sci. China Math. 53, 3255–3278 (2010). https://doi.org/10.1007/s11425-010-4075-7

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  • DOI: https://doi.org/10.1007/s11425-010-4075-7

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