| Boundary Integral Equations and A Posteriori Error Estimates |
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| 引用本文： | 余德浩 赵龙花. Boundary Integral Equations and A Posteriori Error Estimates[J]. 清华大学学报, 2005, 10(1): 35-42. DOI: 10.1016/S1007-0214(05)70006-7 |
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| 作者姓名： | 余德浩 赵龙花 |
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| 作者单位： | InstituteofComputationalMathematicsandScientific／EngineeringComputing,AcademyofMathematicsandSystemScience,ChineseAcademyofSciences,P.O.Box2719,Beijing100080,China |
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| 基金项目： | Supported by the National Key Basic Research and Development(973) Program of China (No. G19990328) and the Knowledge Innovation Program of the Chinese Academy of Sciences |
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| 摘 要： | Adaptive methods have been rapidly developed and applied in many fields of scientific and engineering computing, Reliable and efficient a posteriori error estimates play key roles for both adaptive finite element and boundary element methods. The aim of this paper is to develop a posteriori error estimates for boundary element methods. The standard a posteriori error estimates for boundary element methods are obtained from the classical boundary integral equations. This paper presents hyper-singular a posteriori error estimates based on the hyper-singular integral equations, Three kinds of residuals are used as the estimates for boundary element errors. The theoretical analysis and numerical examples show that the hypersingular residuals are good a posteriori error indicators in many adaptive boundary element computations.
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| 关 键 词： | 工程计算 边界积分方程 后验误差估计 自然边界还原 超奇异残差 拟微分算子 |
| 收稿时间： | 2004-08-02 |
Boundary Integral Equations and A Posteriori Error Estimates |
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| Dehao Yu, ,#xf;,#xfb;,#xd;,Longhua Zhao, ,#xd;,#xf;,#xb;. Boundary Integral Equations and A Posteriori Error Estimates[J]. Tsinghua Science and Technology, 2005, 10(1): 35-42. DOI: 10.1016/S1007-0214(05)70006-7 |
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| Authors: | Dehao Yu, û
,Longhua Zhao,
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| Affiliation: | YU Dehao ZHAO Longhua Institute of Computational Mathematics and Scientific/Engineering Computing,Academy of Mathematics and System Science,Chinese Academy of Sciences,P. O. Box 2719,Beijing 100080,China |
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| Abstract: | Adaptive methods have been rapidly developed and applied in many fields of scientific and engi- neering computing. Reliable and efficient a posteriori error estimates play key roles for both adaptive finite element and boundary element methods. The aim of this paper is to develop a posteriori error estimates for boundary element methods. The standard a posteriori error estimates for boundary element methods are obtained from the classical boundary integral equations. This paper presents hyper-singular a posteriori er- ror estimates based on the hyper-singular integral equations. Three kinds of residuals are used as the esti- mates for boundary element errors. The theoretical analysis and numerical examples show that the hyper- singular residuals are good a posteriori error indicators in many adaptive boundary element computations. |
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| Keywords: | boundary integral equation natural boundary reduction a posteriori error estimate hyper- singular residual pseudo-differential operator |
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