$H^1$ Error Estimates for the Finite Volume Element Method Along Characteristics for Two Dimensional Semiconductor Device with Heat Conduction
二维热传导型半导体器件的特征有限体积元方法和H1模分析

Combined with the method of characteristics, a fully discrete finite volume element method for two dimensional semiconductor device is derived and studied, with piecewise linear function as trial function and piecewise constant as test function. Through convergence analysis an optimal H1 error estimate is obtained under general condition.