标题：A Numerical Approximation Structured by Mixed Finite Element and Upwind Fractional Step Difference for Semiconductor Device with Heat Conduction and Its Numerical Analysis
作者：Yuan Yirang;Yang Qing;Li Changfeng;Sun Tongjun
作者机构：[Yuan Yirang] Institute of Mathematics, Shandong University, Jinan, Shandong 250100, China.;[Sun Tongjun] Institute of Mathematics, Shandong Universit 更多
通讯作者地址：[Yuan, YR]Shandong Univ, Inst Math, Jinan 250100, Peoples R China.
关键词：Three dimensional transient behavior of heat conduction problem;; numerical simulation computation; mixed finite element; modified upwind; fractional step difference; second-order error estimates in L-2 norm
摘要：A coupled mathematical system of four quasi-linear partial differential equations and the initial-boundary value conditions is presented to interpret transient behavior of three dimensional semiconductor device with heat conduction. The electric potential is defined by an elliptic equation, the electron and hole concentrations are determined by convection-dominated diffusion equations and the temperature is interpreted by a heat conduction equation. A mixed finite element approximation is used to get the electric field potential and one order of computational accuracy is improved. Two concentration equations and the heat conduction equation are solved by a fractional step scheme modified by a second-order upwind difference method, which can overcome numerical oscillation, dispersion and computational complexity. This changes the computation of a three dimensional problem into three successive computations of one-dimensional problem where the method of speedup is used and the computational work is greatly shortened. An optimal second-order error estimate in L-2 norm is derived by prior estimate theory and other special techniques of partial differential equations. This type of parallel method is important in numerical analysis and is most valuable in numerical application of semiconductor device and it can successfully solve this international famous problem.