| KdV方程的特征线混合间断有限元方法 |
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| 引用本文： | 文宗川,郭彦,梁静国,李宏.KdV方程的特征线混合间断有限元方法[J].应用数学,2007,20(4):791-800. |
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| 作者姓名： | 文宗川 郭彦 梁静国 李宏 |
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| 作者单位： | 1. 哈尔滨工程大学经济管理学院,黑龙江,哈尔滨,150001
2. 内蒙古大学理工学院数学系,内蒙古,呼和浩特,010021 |
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| 基金项目： | 国家自然科学基金;内蒙古自然科学基金 |
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| 摘 要： | 考虑KdV方程的两种特征线性混合间断有限元方法,一种方法建立在标准特征线修正方法的基础上,另一种方法是带有对流项修正的特征线修正方法.利用具有实际物理意义的特征线追踪技巧处理时间导数项和对流项,采用混合间断有限元方法处理三阶导数项,分别证明了两种方法有限元解的唯一性、稳定性和误差估计.
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| 关 键 词： | KdV方程 混合间断有限元方法 特征线修正方法 带有对流项修正的特征线修正方法 |
| 文章编号： | 1001-9847（2007）04-0791-10 |
| 修稿时间： | 2007-04-26 |
The Characteristic Mixed Discontinuous Finite Element Method for KdV Eqation |
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| WEN ZONG-chuan,GUO Yan,LIANG Jing-guo,LI Hong.The Characteristic Mixed Discontinuous Finite Element Method for KdV Eqation[J].Mathematica Applicata,2007,20(4):791-800. |
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| Authors: | WEN ZONG-chuan GUO Yan LIANG Jing-guo LI Hong |
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| Institution: | School of Economics and Management,Harbin Engineering University,Harbin 150001,China;College of Sciences and Technology,Department of Mathematics,Neimongol University,Huhhot 010021,China;School of Economics and Management,Harbin Engineering University,Harbin 150001,China;College of Sciences and Technology,Department of Mathematics,Neimongol University,Huhhot 010021,China |
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| Abstract: | Two characteristic mixed discontinuous finite element methods are introduced for KdV equation.The first method iS based on the standard modified method of characteristics(MMOC).The second method is formulated using the modified method of characteristics with adjusted advection (MMOCAA).The temporal differentiation and advection terms are treated by a physical,characteristic tracking technique.The third derivatives are discretized by mixed discontinuous finite element method.The uniqueness and stability for each method is obtained,and the error estimates are established respectively. |
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| Keywords: | KdV equation Mixed discontinuous finite element method Modified method of characteristics Modified method of characteristics with adjusted advection |
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