标题：An Approximation of Three-Dimensional Semiconductor Devices by Mixed Finite Element Method and Characteristics-Mixed Finite Element Method
作者：Yang, Qing; Yuan, Yirang
作者机构：[Yang Qing] School of Mathematical Science, Shandong Normal University, Jinan, Shandong 250014, China.;[Yuan Yirang] Institute of Mathematics, Shandon 更多
通讯作者地址：[Yang, Q]Shandong Normal Univ, Sch Math Sci, Jinan 250014, Peoples R China.
关键词：Three-dimensional semiconductor devices; characteristics-mixed finite; element method; mixed finite element method; post-processing step; error; bound
摘要：The mathematical model for semiconductor devices in three space dimensions are numerically discretized. The system consists of three quasi-linear partial differential equations about three physical variables: the electrostatic potential, the electron concentration and the hole concentration. We use standard mixed finite element method to approximate the elliptic electrostatic potential equation. For the two convection-dominated concentration equations, a characteristics-mixed finite element method is presented. The scheme is locally conservative. The optimal L-2-norm error estimates are derived by the aid of a post-processing step. Finally, numerical experiments are presented to validate the theoretical analysis.