Volume 24, Issue 3
Optimal Error Estimates of the Partition of Unity Method with Local Polynomial Approximation Spaces

Yun-Qing Huang, Wei Li & Fang Su

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J. Comp. Math., 24 (2006), pp. 365-372.

Published online: 2006-06

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  • Abstract

In this paper, we provide a theoretical analysis of the partition of unity finite element method(PUFEM), which belongs to the family of meshfree methods. The usual error analysis only shows the order of error estimate to the same as the local approximations\cite{p1}. Using standard linear finite element base functions as partition of unity and polynomials as local approximation space, in 1-d case, we derive optimal order error estimates for PUFEM interpolants. Our analysis show that the error estimate is of one order higher than the local approximations. The interpolation error estimates yield optimal error estimates for PUFEM solutions of elliptic boundary value problems.

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Meshless methods Partition of unity finite element method(PUFEM) Error estimate

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@Article{JCM-24-365, author = {}, title = {Optimal Error Estimates of the Partition of Unity Method with Local Polynomial Approximation Spaces}, journal = {Journal of Computational Mathematics}, year = {2006}, volume = {24}, number = {3}, pages = {365--372}, abstract = { In this paper, we provide a theoretical analysis of the partition of unity finite element method(PUFEM), which belongs to the family of meshfree methods. The usual error analysis only shows the order of error estimate to the same as the local approximations\cite{p1}. Using standard linear finite element base functions as partition of unity and polynomials as local approximation space, in 1-d case, we derive optimal order error estimates for PUFEM interpolants. Our analysis show that the error estimate is of one order higher than the local approximations. The interpolation error estimates yield optimal error estimates for PUFEM solutions of elliptic boundary value problems. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8758.html} }
TY - JOUR T1 - Optimal Error Estimates of the Partition of Unity Method with Local Polynomial Approximation Spaces JO - Journal of Computational Mathematics VL - 3 SP - 365 EP - 372 PY - 2006 DA - 2006/06 SN - 24 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8758.html KW - Meshless methods KW - Partition of unity finite element method(PUFEM) KW - Error estimate AB - In this paper, we provide a theoretical analysis of the partition of unity finite element method(PUFEM), which belongs to the family of meshfree methods. The usual error analysis only shows the order of error estimate to the same as the local approximations\cite{p1}. Using standard linear finite element base functions as partition of unity and polynomials as local approximation space, in 1-d case, we derive optimal order error estimates for PUFEM interpolants. Our analysis show that the error estimate is of one order higher than the local approximations. The interpolation error estimates yield optimal error estimates for PUFEM solutions of elliptic boundary value problems.
Yun-Qing Huang, Wei Li & Fang Su. (1970). Optimal Error Estimates of the Partition of Unity Method with Local Polynomial Approximation Spaces. Journal of Computational Mathematics. 24 (3). 365-372. doi:
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