复变量移动最小二乘近似在Sobolev空间中的误差估计

孙新志; 李小林

doi:10.3879/j.issn.1000-0887.2016.04.009

复变量移动最小二乘近似在Sobolev空间中的误差估计

doi: 10.3879/j.issn.1000-0887.2016.04.009

重庆师范大学数学科学学院, 重庆 401331

基金项目: 国家自然科学基金（面上项目）（11471063）

详细信息

作者简介:
孙新志（1992—），男，硕士生（E-mail: 271735206@qq.com）;李小林（1983—），男，教授，博士（通讯作者. E-mail: lxlmath@163.com）.

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出版历程
- 收稿日期: 2015-12-11
- 修回日期: 2016-01-13
- 刊出日期: 2016-04-15

Error Estimates for the Complex Variable Moving Least Square Approximation in Sobolev Spaces

School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, P.R.China

Funds: The National Natural Science Foundation of China（General Program）（11471063）

摘要

摘要: 复变量移动最小二乘近似是形成无网格法形函数的重要方法，为了研究相应的无网格方法的误差估计，需要先分析复变量移动最小二乘近似的逼近误差.首先介绍了复变量移动最小二乘近似，接着在权函数满足一定假设的条件下，详细讨论了复变量移动最小二乘近似逼近函数在Sobolev空间中的误差估计，给出了逼近函数在H^k范数下的误差界，分析结果表明逼近函数的误差随着节点间距的减小而降低.最后给出了一个数值算例来验证理论分析的正确性.
- 复变量移动最小二乘近似 /
- 无网格法 /
- Sobolev空间 /
- 误差分析
Abstract: The complex variable moving least square (CVMLS) approximation is an important approach to construct shape functions in the meshless method. For the error analysis of the CVMLS-based meshless method, it is fundamental to conduct error estimates of the CVMLS approximation in Sobolev spaces. First an introduction of the CVMLS was given. Then, the error estimates of the CVMLS in Sobolev spaces with weight functions satisfying specific conditions were obtained. The error bounds of the approximation functions in H^k norm were given. Finally, a numerical example was given to verify the validity of the theoretical analysis. The results show that the errors will decrease as the nodal spacings reduce.
- complex variable moving least square approximation /
- meshless method /
- Sobolev space /
- error analysis

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参考文献(23)

[1]	Lancaster P, Salkauskas K. Surface generated by moving least square methods[J].Mathematics of Computation,1981,37(155): 141-158.
[2]	Belytschko T, Lu Y Y, Gu L. Element-free Galerkin methods[J].International Journal for Numerical Methods in Engineering,1994,37(2): 229-256.
[3]	张小华, 邓霁恒. 三维稳态对流扩散问题的无网格求解算法研究[J]. 应用数学和力学, 2014,35(11): 1249-1258.(ZHANG Xiao-hua，DENG Ji-heng. Research on the meshless solving algorithm for 3D steady convection-diffusion problems[J].Applied Mathematics and Mechanics,2014,35(11): 1249-1258.(in Chinese))
[4]	王伟, 伊士超, 姚林泉. 分析复合材料层合板弯曲和振动的一种有效无网格方法[J]. 应用数学和力学, 2015,36(12): 1274-1284.(WANG Wei, YI Shi-chao,YAO Lin-quan. An effective meshfree method for bending and vibration analyses of laminated composite plates[J].Applied Mathematics and Mechanics,2015,36(12): 1274-1284.(in Chinese))
[5]	程玉民, 彭妙娟, 李九红. 复变量移动最小二乘法及其应用[J]. 力学学报, 2005,37(6): 719-723.（CHENG Yu-min, PENG Miao-juan, LI Jiu-hong. The complex variable moving least-square approximation and its application[J].Chinese Journal of Theoretical and Applied Mechanics,2005,37(6): 719-723.(in Chinese)）
[6]	Liew K M, Feng C, Cheng Y M, Kitipornchai S. Complex variable moving least-squares method: a meshless approximation technique[J].International Journal for Numerical Methods in Engineering,2007,70(1): 46-70.
[7]	Chen L, Cheng Y M. The complex variable reproducing kernel particle method for elasto-plasticity problems[J].Science China Physics Mechanics & Astronomy,2010,53(5): 954-965.
[8]	Zhang L W, Deng Y J, Liew K M, Cheng Y M. The improved complex variable element-free Galerkin method for two-dimensional Schrdinger equation[J].Computers & Mathematics With Applications,2014,68(10): 1093-1106.
[9]	Levin D. The approximation power of moving least-squares[J].Mathematics of Computation,1998,67(224): 1517-1531.
[10]	Armentano M G, Durán R G. Error estimates for moving least square approximations[J].Applied Numerical Mathematics,2001,37(3): 397-416.
[11]	Armentano M G. Error estimates in Sobolev spaces for moving least square approximations[J].Society for Industrial & Applied Mathematics,2001,39(1): 38-51.
[12]	Zuppa C. Error estimates for moving least square approximations[J].Bulletin of the Brazilian Mathematical Society,2003,34(2): 231-249.
[13]	CHENG Rong-jun, CHENG Yu-min. Error estimates for the finite point method[J].Applied Numerical Mathematics,2008,58(6): 884-898.
[14]	Zuppa C. Good quality point sets and error estimates for moving least square approximations[J].Bulletin Brazilian Mathematical Society,2003,47(3): 575-585.
[15]	LI Xiao-lin, ZHU Jia-lin. A Galerkin boundary node method and its convergence analysis[J].Journal of Computational & Applied Mathematics,2009,230(1): 314-328.
[16]	LI Xiao-lin. Meshless Galerkin algorithms for boundary integral equations with moving least square approximations[J].Applied Numerical Mathematics,2011,61(12): 1237-1256.
[17]	Wang J F, Sun F X, Cheng Y M, Huang A X. Error estimates for the interpolating moving least-squares method inn-dimensional space[J].Applied Numerical Mathematics,2015,98: 79-105.
[18]	LI Xiao-lin, CHEN Hao, WANG Yan. Error analysis in Sobolev spaces for the improved moving least-square approximation and the improved element-free Galerkin method[J].Applied Mathematics and Computation,2015,262: 56-78.
[19]	LI Xiao-lin. Error estimates for the moving least-square approximation and the element free Galerkin method inn -dimensional spaces[J].Applied Numerical Mathematics.2016,99(C): 77-97.
[20]	张贤科. 高等代数学[M]. 北京: 清华大学出版社, 1998.(ZHANG Xian-ke.Advanced Algebra [M]. Beijing: Tsinghua University Press, 1998.(in Chinese))
[21]	HAN Wei-min, MENG Xue-ping. Error analysis of the reproducing kernel particle method[J].Computer Methods in Applied Mechanics and Engineering,2001,190(46/47): 6157-6181.
[22]	Brenner S C, Scott L R.The Mathematical Theory of Finite Element Methods[M]. New York: Springer, 2002.
[23]	Lions L, Magenes E.Non-Homogeneous Boundary Value Problems and Applications[M]. Berlin: Springer, 1972: 227-308.

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复变量移动最小二乘近似在Sobolev空间中的误差估计

doi: 10.3879/j.issn.1000-0887.2016.04.009

作者简介:
孙新志（1992—），男，硕士生（E-mail: 271735206@qq.com）;李小林（1983—），男，教授，博士（通讯作者. E-mail: lxlmath@163.com）.

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Error Estimates for the Complex Variable Moving Least Square Approximation in Sobolev Spaces

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复变量移动最小二乘近似在Sobolev空间中的误差估计

doi: 10.3879/j.issn.1000-0887.2016.04.009

作者简介: 孙新志（1992—），男，硕士生（E-mail: 271735206@qq.com）;李小林（1983—），男，教授，博士（通讯作者. E-mail: lxlmath@163.com）.

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出版历程

Error Estimates for the Complex Variable Moving Least Square Approximation in Sobolev Spaces

计量

出版历程

目录

作者简介:
孙新志（1992—），男，硕士生（E-mail: 271735206@qq.com）;李小林（1983—），男，教授，博士（通讯作者. E-mail: lxlmath@163.com）.