三维热传导型半导体问题的特征有限元方法和分析

本文研究三维热传导型半导体瞬态问题的特征有限元方法及其理论分析，其数学模型是一类非线性偏微分方程的初边值问题，对电子位势方程提出Ｇａｌｅｒｋｉｎ逼近；对电子，空穴浓度方程采用特征有限元逼近；对热传导方程采用对时间向后差分的Ｇａｌｅｒｋｉｎ逼近．应用微分方程先验估计理论和技巧得到了最优阶Ｌ＾２误差估计。

CHARACTERISTIC FINITE ELEMENT METHOD AND ANALYSIS FOR THE THREE-DIMENSIONAL SEMICONDUCTOR PROBLEM WITH HEAT-CONDUCTION

Characteristic finite element method is introduced and analyzed for approximating the solution of three\|dimensional transient behavior of semiconductor with heat\|conduction, whose mathematical model is an initial and boundary value problem of nonlinear partial differential equation system. Electric potential and heat\|conduction equations are approximated by a Galerkin procedure, electron and hole concentration is approximated by the characteristic finite element method. Optimal order error estimates in L\ 2 are demonstrated.