| 双相滞热传导方程的有限元分析 |
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| 引用本文： | 江成顺,姚俐,刘蕴贤. 双相滞热传导方程的有限元分析[J]. 计算数学, 2005, 27(1): 31-44 |
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| 作者姓名： | 江成顺 姚俐 刘蕴贤 |
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| 作者单位： | 信息工程大学信息工程学院,郑州,450002;大连理工大学海岸与近海工程国家重点实验室,大连,116024;信息工程大学信息工程学院,郑州,450002;山东大学数学学院,济南,250100 |
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| 基金项目： | 国家自然科学基金数学天元基金资助课题(A0324647)河南省高校杰出科研人才创新工程基金资助项目(2003KJCX008)大连理工大学近海与海岸工程国家重点实验室科学基金项目(LP200201). |
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| 摘 要： | 本文考虑一类具有广泛应用背景的双相滞热传导方程混合边界问题．建立了其有限元和交替方向有限元的两种数值逼近格式．利用微分方程的先验估计理论与技巧，作出了数值解的L^2—范数估计结果．基于一系列的误差估计，也研究了两种逼近格式数值的稳定性和收敛性。
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| 关 键 词： | 双相滞热传导方程 有限元方法 误差估计 稳定性分析 |
FINITE ELEMENT ANALYSIS FOR DUAL PHASE LAGGING HEAT CONDUCTION EQUATIONS |
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| Jiang Chengshun. FINITE ELEMENT ANALYSIS FOR DUAL PHASE LAGGING HEAT CONDUCTION EQUATIONS[J]. Mathematica Numerica Sinica, 2005, 27(1): 31-44 |
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| Authors: | Jiang Chengshun |
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| Affiliation: | Jiang Chengshun(Institute of Information Engineering, Information Engineering University, Zhenzhou 450002; State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology,Dalian 116024)Yao Li(Institute of Information Engineering, Information Engineering University,Zhengzhou 450002)Liu Yunxian (School of Mathematics, Shandong University, Jinan 250100) |
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| Abstract: | This paper is concerned with the mixed boundary problems of dual-phase-lagging heat conduction equations arising in many fields. A finite element numerical approximation scheme and an alternating direction finite element approximation scheme are established. The optimal error estimation of L2-norm is made for the approximationsolution by the prior estimation theory and the technique of differential equations. The convergency and stability of the two schemes are also demonstrated based on a series of error estimation. |
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| Keywords: | dual - phase - lagging heat conduction equations finite element scheme error estimation stability analysis. |
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