半导体问题的交替方向有限元方法

该文用交替方向有限元方法求解半导体问题的Energy Trans port (ET)模型。对模型中椭圆型的电子位势方程采用交替方向迭代法，对流占优扩散的电子浓度和空穴浓度方程采用特征交替方向有限元方法，热传导方程利用Patch逼近采用交替方向有限元方法求解。利用微分方程的先验估计理论和技巧，分别得到了椭圆型方程和抛物型方程的最优H+1和L+2误差估计。

Alternating Direction Finite Element Method for Semiconductor Problem

The energy transport model of semiconductor problem, including both elliptic and parabolic equations, is solved by an alternating direction method. The elliptic equation for the electrostatic potential is solved by an alternating direction iterative method, the convection-dominated diffusion equations for the conservation of electron and hole concentrations are solved by an characteristic alternating direction finite element method, and the heat conduction equation is solved by an alternating direction finite element method with patch approximation. Using the theory and technique of a priori estimate of differential equation, the author obtains the optimal order error estimates in H^1-norm and L^2-norm of the elliptic equation and parabolic equations respectively.