半导体问题的特征有限元方法和H^1模估计

Characteristic Element Methods and H^1 Error Estimates for the Semiconductor Problem

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H1误差估计。

Characteristic element methods are introduced and analyzed for approximating the solutions of three-dimensional transient behavior of semiconductor with heat-conduction, whose mathematical model is initial and boundary problem of nonlinear partial differential equation system. Electric potential and heat-conduction equation are approximated by a Galerkin procedures. electron and hole concentrations are approximated by characteristic element methods. Optimal order error estimates in H^1 are demonstrated.