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In this paper, based on the natural boundary reduction advanced by Feng and Yu, we couple the finite element approach with the natural boundary element method to study the weak solvability and Galerkin approximation of a class of nonlinear exterior boundary value problems. The analysis is mainly based on the variational formulation with constraints. We prove the error estimate of the finite element solution and obtain the asymptotic rate of convergence. Finally, we also give a numerical example.
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计算数学与科学工程计算及其在中国的若干发展 (迎接ICM2002特约文章) 总被引:15,自引:0,他引:15
本文论述了计算数学与科学工程计算的重要性,回顾了近50年来这一学科在中国的发展,特别是冯康的杰出贡献,介绍了国家重点基础研究发展规划相关项目的研究课题。 相似文献
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椭圆边界上的自然积分算子及各向异性外问题的耦合算法 总被引:10,自引:5,他引:10
1.引 言为求解微分方程的外边值问题常需要引进人工边界(见[1-4]),对人工边界外部区域作自然边界归化得到的自然积分方程即Dirichlet-Neumann映射,正是人工边界上的准确的边界条件(见[2-6]),这是一类非局部边界条件.自然积分算子即Dirichlet-Neumann算子, 相似文献
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The artificial boundary method is applied to solve three-dimensional exterior problems. Two kind of rotating ellipsoids are chosen as the artificial boundaries and the exact artificial boundary conditions are derived explicitly in terms of an infinite series. Then the well-posedness of the coupled variational problem is obtained. It is found that error estimates derived depend on the mesh size, truncation term and the location of the artificial boundary. Three numerical examples are presented to demonstrate the effectiveness and accuracy of the proposed method. 相似文献
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De-haoYu 《计算数学(英文版)》2004,22(2):309-318
In this paper, the natural boundary integral method, and some related methods, including coupling method of the natural boundary elements and finite elements, which is also called DtN method or the method with exact artificial boundary conditions, domain decomposition methods based on the natural boundary reduction, and the adaptive boundary element method with hyper-singular a posteriori error estimates, are discussed. 相似文献
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Deng Zilong Zhang Chengbin Sun Qing Wu Liangyu Yao Feng Xu Dehao 《Journal of Thermal Analysis and Calorimetry》2021,144(3):869-882
Journal of Thermal Analysis and Calorimetry - Efficient thermal management has become an important challenge for the integration and miniaturization of electronic devices with high power density.... 相似文献
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In this paper, based on the natural boundary reduction advanced by Feng and Yu, we couple the finite element approach with the natural boundary element method to study the weak solvability and Galerkin approximation of a class of nonlinear exterior boundary value problems. The analysis is mainly based on the variational formulation with constraints. We prove the error estimate of the finite element solution and obtain the asymptotic rate of convergence. Finally, we also give a numerical example. 相似文献
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三维Helmholtz方程外问题的自然边界元与有限元耦合法 总被引:4,自引:0,他引:4
1.引言 设Γ0是空间闭曲面,Ω是Γ0外部的无界区域,考虑三维Helmholtz 方程外Neumann问题其中 是波数,w是频率,c0为波在均匀介质中的传播速度,v是区域Ω的边界Γ0的外法线方向,即指向由 Γ0包围的内部区域, 为 Γ0上的已知函数.为了保证问题(1.1)和(1.2)的解的存在唯一性,必须附加上无穷远边界条件,即所谓的 Sommerfeld辐射条件其中i是虚数单位, . 许多数学物理问题,例如时间调和声波对不可穿透的障碍物的散射,海洋水下声波的传播,电磁波的绕射与辐… 相似文献