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An adaptive local maximum entropy point collocation method for linear elasticity

Fan, L. and Coombs, W.M. and Augarde, C.E. (2021) 'An adaptive local maximum entropy point collocation method for linear elasticity.', Computers and structures., 256 . p. 106644.


Point collocation methods are strong form approaches that can be applied to continuum mechanics problems and possess attractive features over weak form-based methods due to the absence of a mesh. While various adaptive strategies have been proposed to improve the accuracy of weak form-based methods, such techniques have received little attention for strong form-based methods. In this paper, combined rh-adaptivity, in which r- and h-adaptivities are adopted iteratively, is applied to the local maximum entropy point collocation method for the first time to solve linear elasticity problems. Material force residuals act as driving forces in r-adaptivity to relocate collocation points, reducing the error associated with a given point distribution. Physical equilibrium residuals are used as the error estimator in h-adaptivity to determine the insertion locations for new points, diminishing the error caused by inadequate degrees of freedom. Issues arising in mesh-based methods, such as mesh distortion and hanging nodes, are entirely absent from the proposed method. The paper introduces the approach for the rst time and the study is therefore conned to 2D domains. Numerical examples are presented to demonstrate the performance of the proposed adaptive strategies, comparing convergence rates and computational costs using uniform renement, pure r-, h- and combined rh-adaptivities.

Item Type:Article
Full text:Publisher-imposed embargo until 10 August 2023.
(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives 4.0.
File format - PDF
Publisher Web site:
Publisher statement:© 2021 This manuscript version is made available under the CC-BY-NC-ND 4.0 license
Date accepted:20 July 2021
Date deposited:20 July 2021
Date of first online publication:10 August 2021
Date first made open access:10 August 2023

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