标题：Analysis of the local discontinuous Galerkin method for the drift-diffusion model of semiconductor devices
作者：Liu YunXian; Shu Chi-Wang
作者机构：[Liu Yunxian] School of Mathematics, Shandong University, Jinan, Shandong 250100, China.;[Shu Chiwang] Division of Applied Mathematics, Brown Universi 更多
通讯作者地址：[Shu, CW]Brown Univ, Div Appl Math, Providence, RI 02912 USA.
关键词：local discontinuous Galerkin method; semi-discrete; implicit-explicit; scheme; error estimate; semiconductor
摘要：We consider the drift-diffusion (DD) model of one dimensional semiconductor devices, which is a system involving not only first derivative convection terms but also second derivative diffusion terms and a coupled Poisson potential equation. Optimal error estimates are obtained for both the semi-discrete and fully discrete local discontinuous Galerkin (LDG) schemes with smooth solutions. In the fully discrete scheme, we couple the implicit-explicit (IMEX) time discretization with the LDG spatial discretization, in order to allow larger time steps and to save computational cost. The main technical difficulty in the analysis is to treat the inter-element jump terms which arise from the discontinuous nature of the numerical method and the nonlinearity and coupling of the models. A simulation is also performed to validate the analysis.