Optimal Error Estimates of the Partition of Unity Method with Local Polynomial Approximation Spaces

Optimal Error Estimates of the Partition of Unity Method with Local Polynomial Approximation Spaces

Year:    2006

Journal of Computational Mathematics, Vol. 24 (2006), Iss. 3 : pp. 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 [12]. 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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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2006-JCM-8758

Journal of Computational Mathematics, Vol. 24 (2006), Iss. 3 : pp. 365–372

Published online:    2006-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    8

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