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

SUN Xin-zhi; LI Xiao-lin

doi:10.3879/j.issn.1000-0887.2016.04.009

Volume 37 Issue 4

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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

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

doi: 10.3879/j.issn.1000-0887.2016.04.009

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

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

Received Date: 2015-12-11
Rev Recd Date: 2016-01-13
Publish Date: 2016-04-15

Abstract

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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References(23)

References

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