| 一类二维非局部椭圆问题的有限元方法 |
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| 引用本文： | 周鸿旋,喻海元,聂存云. 一类二维非局部椭圆问题的有限元方法[J]. 湘潭大学自然科学学报, 2010, 32(3) |
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| 作者姓名： | 周鸿旋 喻海元 聂存云 |
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| 作者单位： | 闽江学院软件学院;湘潭大学数学与计算科学学院;湖南工程学院理学院; |
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| 基金项目： | 国家自然科学基金,湖南省科技厅一般项目,国家自然科学基金,湖南省高校科技创新团队支持计划资助项目 |
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| 摘 要： | 针对一类具有非局部边界的二维椭圆问题,利用微分方程的叠加原理,将方程化为带Dirichlet边界的非齐次方程和带积分边界的齐次方程,采用等参双线性有限元方法分别进行离散,得到该问题的有限元解;进一步,对相应有限元解进行误差分析,得到其最优L2模估计,数值实验验证了理论结果的正确性.
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| 关 键 词： | 非局部边界 椭圆问题 等参双线性有限元 误差估计 |
A Finite Element Method for Two Dimension Elliptic Problem with Nonlocal Boundary Conditions |
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| ZHOU Hong-xuan,YU Hai-yuan,NIE Cun-yun. A Finite Element Method for Two Dimension Elliptic Problem with Nonlocal Boundary Conditions[J]. Natural Science Journal of Xiangtan University, 2010, 32(3) |
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| Authors: | ZHOU Hong-xuan YU Hai-yuan NIE Cun-yun |
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| Affiliation: | ZHOU Hong-xuan1,YU Hai-yuan2,NIE Cun-yun2,3(1.Software College,Minjiang University,Fuzhou 350011,2.College of Mathematics and Computational Science,Xiangtan University,Xiangtan 411105,3.Department of Mathematics and Physics,Hunan Institute of Engineering,Xiangtan 411104 China) |
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| Abstract: | The two dimension elliptic problem with nonlocal boundary conditions is firstly decomposed into two subproblems: nonhomogeneous one with Dirichlet boundary and homogeneous one with nonlocal boundary.The isoparametric bilinear finite element method is applied for the two subproblems above,and the corresponding finite element solutions are obtained.Furthermore,the optimal error estimates in the norm L2 are derived.Finally,Numerical experiment verifies the theoretical results. |
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| Keywords: | nonlocal boundary conditions elliptic problem the isoparametric bilinear finite element error estimates |
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