| 二阶椭圆型方程边值问题的变分原理研究 |
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| 引用本文： | 李建斌,李欣,蔡靖疆,何永斌.二阶椭圆型方程边值问题的变分原理研究[J].成都理工大学学报(自然科学版),2004,31(3):325-330. |
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| 作者姓名： | 李建斌 李欣 蔡靖疆 何永斌 |
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| 作者单位： | 华为技术有限公司,深圳,518129;攀枝花学院理学系;北京中兴通讯股份有限公司 |
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| 摘 要： | 利用变分法研究了二阶椭圆型方程混合边值问题的变分原理,论证了最小位能原理和虚功原理.在古典解的条件下,边值问题、变分问题和变分方程是等价的;但变分问题和变分方程还存在边值问题的广义解.文章最后利用变分原理和分片多项式插值相结合的有限元法,给出了一个典型算例.
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| 关 键 词： | 变分法 极小位能原理 虚功原理 分片多项式插值 |
| 文章编号： | 1671-9727(2004)03-0325-06 |
| 修稿时间： | 2003年3月22日 |
Research of variation principle about boundary value problem of second order elliptic differential equation |
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| LI Jian-bin,LI Xin,CAI Jing-jiang,HE Yong-bin.Research of variation principle about boundary value problem of second order elliptic differential equation[J].Journal of Chengdu University of Technology: Sci & Technol Ed,2004,31(3):325-330. |
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| Authors: | LI Jian-bin LI Xin CAI Jing-jiang HE Yong-bin |
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| Institution: | LI Jian-bin~1,LI Xin~2,CAI Jing-jiang~3,HE Yong-bin~2 |
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| Abstract: | This paper studies the variation principle about the mixed boundary value problem of second (order) elliptic differential equation by the calculus of variation and strictly testifies the principle of minimum potential energy and the principle of virtual work. Under the condition of classic solution, the boundary value problem, variation problem and variation equation are equivalent. But there exists generalized (solution) of the boundary value problem between variation probem and variation equation. At last, a model example is supplied by the finite element method which is combined by variation principle and piecewise polynomial interpolation. |
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| Keywords: | calculus of variation principle of minimum potential energy principle of virtual work (piecewise) polynomial interpolation |
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