Error analysis in Sobolev spaces for the improved moving least-square approximation and the improved element-free Galerkin method
Error analysis in Sobolev spaces for the improved moving least-square approximation and the improved element-free Galerkin method
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DOI：
10.1016/j.amc.2015.04.002
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发表时间：
2015-07
期刊：
影响因子：
--
通讯作者：
Xiaolin Li;Hao Chen;Yan Wang
中科院分区：
文献类型：
--
作者：
Xiaolin Li;Hao Chen;Yan Wang
改进的移动最小二乘法(IMLS)是无网格法中构造形函数的一种方法。为了将基于IMLS的无网格法应用于边值问题的数值求解，对Sobolev空间中IMLS逼近的误差进行分析是非常重要的。本文首先讨论了IMLS形函数的性质。在适当的权函数假设下，在多维Soblev空间中建立了IMLS逼近的误差估计。改进的无网格Galerkin(IEFG)方法是一种典型的基于IMLS近似和Galerkin弱形式耦合的无网格Galerkin方法。给出了IEFG方法的误差分析。最后给出了数值算例，验证了理论误差结果。
The improved moving least-square (IMLS) approximation is a method to form shape functions in meshless methods. For the application of IMLS-based meshless methods to the numerical solution of boundary value problems, it is fundamental to analyze error of the IMLS approximation in Sobolev spaces. This paper begins by discussing properties of the IMLS shape function. Under appropriate assumption on weight functions, error estimates for the IMLS approximation are then established in Sobolev spaces in multiple dimensions. The improved element-free Galerkin (IEFG) method is a typical meshless Galerkin method based on coupling the IMLS approximation and Galerkin weak form. Error analysis of the IEFG method is also provided. Numerical examples are finally presented to prove the theoretical error results.