三维热传导型半导体问题的特征混合元方法和分析  

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

作　　者：刘蕴贤[1] 

机构地区：[1]山东大学数学学院,济南250100

出　　处：《应用数学学报》1999年第3期422-432,共11页Acta Mathematicae Applicatae Sinica

摘　　要：本文研究三维热传导型半导体瞬态问题的特征混合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混合元逼近；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L2误差估计．Characteristic mixed finite element method is introduced and analyzed for approximating the solution of three-d;mensional transient behavior of semiconductor with heatconduction, whose mathematical model is initial and boundary problem of nonlinear partial differential equation system. Electric potential equation is approximated by mixed finite element method, electron and hole concentration are approximated by characteristic finite element method, heat-conduction equation is approximated by a Galerkin procedure. Optimal order error estimates in L2 are demonstrated.

关 键 词：特征混合元 热传导 偏微分方程 半导体 瞬态问题 

分 类 号：O471[理学—半导体物理] O241.82[理学—物理]