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《Journal of Chengdu University of Technology(Science & Technology Edition)》 2004-03
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Research of variation principle about boundary value problem of second order elliptic differential equation

LI Jian-bin~1, LI Xin~2, CAI Jing-jiang~3, HE Yong-bin~2 (1.Huawei Technical Limite Company, Shenzhen, China; 2.Panzhihua Institute, Sichuan, China; 3.ZTE Limited Company, Beijing)  
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.
【CateGory Index】: O175.25
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【Co-citations】
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1 KANG Tong,CHEN Tao,TU Zhong-hua,ZHAO Meng-zhou(Department of Applied Mathematics,School of Sciences,Communication University of China,Beijing 100024,Chian);A Finite Element Method for Solving Two-dimensional Time-harmonic Scattering Problems with Perfectly Matched Layer[J];Journal of Communication University of China(Science and Technology);2009-03
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