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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

孙新志 李小林

孙新志, 李小林. 复变量移动最小二乘近似在Sobolev空间中的误差估计[J]. 应用数学和力学, 2016, 37(4): 416-425. doi: 10.3879/j.issn.1000-0887.2016.04.009
引用本文: 孙新志, 李小林. 复变量移动最小二乘近似在Sobolev空间中的误差估计[J]. 应用数学和力学, 2016, 37(4): 416-425. doi: 10.3879/j.issn.1000-0887.2016.04.009
SUN Xin-zhi, LI Xiao-lin. Error Estimates for the Complex Variable Moving Least Square Approximation in Sobolev Spaces[J]. Applied Mathematics and Mechanics, 2016, 37(4): 416-425. doi: 10.3879/j.issn.1000-0887.2016.04.009
Citation: SUN Xin-zhi, LI Xiao-lin. Error Estimates for the Complex Variable Moving Least Square Approximation in Sobolev Spaces[J]. Applied Mathematics and Mechanics, 2016, 37(4): 416-425. 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
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).

  • 中图分类号: O242.2

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

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

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