| 半导体问题的特征有限元方法和H1模估计 |
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| 引用本文： | 刘蕴贤.半导体问题的特征有限元方法和H1模估计[J].工程数学学报,2003,20(6):7-13. |
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| 作者姓名： | 刘蕴贤 |
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| 作者单位： | 山东大学数学与系统科学学院,济南,250100 |
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| 基金项目： | 国家自然科学基金，国家自然科学基金，，TY10126029，， |
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| 摘 要： | 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H^1误差估计。
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| 关 键 词： | 特征有限元 半导体瞬态 热传导 最优误差估计 |
| 文章编号： | 1005-3085(2003)06-0007-07 |
Characteristic Element Methods and H1 Error Estimates for the Semiconductor Problem |
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| LIU Yun-xian.Characteristic Element Methods and H1 Error Estimates for the Semiconductor Problem[J].Chinese Journal of Engineering Mathematics,2003,20(6):7-13. |
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| Authors: | LIU Yun-xian |
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| Abstract: | 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. |
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| Keywords: | transient behavior of semiconductor heat-conduction characteristic element optimal error estimate |
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