中文摘要：

一半导体器件的瞬时状态由包含三个拟线性偏微分方程所组成的方程组的初边值问题来描述。其中电子位势方程是椭圆型的，电子和空穴浓度方程是对流扩散型的．作者对三维半导体模型问题采甩四面体网格上的有限体积元方法进行逼近，具体地，对电子位势方程采用一次元有限体积法来逼近，对电子浓度和空穴浓度方程采用迎风有限体积方法来逼近，并进行了详细的理论分析，得到了O（h＋△t）阶的L^2模误差估计结果．

英文摘要：

The mathematical model of the semiconductor device is described by the initial boundary value problem for a system of three quasilinear partial differential equations： one of elliptic type for the electrostatic potential, the other two of convection-dominated diffusion type for the conservation of electron and hole concentrations. For 3-d semiconductor device, the electrostatic potential equation is approximated with the aid of finite volume method, while the electron and hole concentration equations are approximated with upwind finite volume schemes. Error estimate of order O（h ＋△At） in L^2-norm is obtained.