热传导型半导体问题的配置方法及误差分析

Collocation Methods and Error Analysis for the Semiconductor Problem with Heat-Conduction

热传导型半导体瞬态问题的数学模型是一类非线性偏微分方程的初边值问题 .电子位势方程是椭圆型的 ,电子、空穴浓度方程及热传导方程是抛物型的 .该文给出求解的配置方法 ,得到次优 L2模误差估计 ,并将配置法和

The mathematical model of the semiconductor device with heat-conduction is described by a initial and boundary problem of nonlinear partial differential equation system. One elliptic equation is for the electric potential, and three parabolic equations are for the electron concentration, hole concentration and temperature. In this paper,collocation methods are put forward, almost optimal error estimates in \$L\+2\$-norm are derived, and numerical results are given to compare the collocation method with the Galerkin finite element method.