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|Title:||Local refinement of flat‐top partition of unity based high‐order approximation||Authors:||Liu, Xiaoying
|Keywords:||Engineering::Civil engineering||Issue Date:||2018||Source:||This is the peer reviewed version of the following article: Liu, X., Zhao, Z., An, X., & Jiao, Y. (2018). Local refinement of flat-top partition of unity based high-order approximation. International Journal for Numerical Methods in Engineering, 116(7), 465-486. doi:10.1002/nme.5932, which has been published in final form at https://doi.org/10.1002/nme.5932. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.||Journal:||International Journal for Numerical Methods in Engineering||Abstract:||The high‐order approximation with regularly patterned flat‐top partition of unity mesh in one‐ and two‐dimensional cases has been proven linearly independent. However, for problems with stress concentration or stress singularity, local refinement within the regular mesh is necessary to improve the accuracy and efficiency. This paper introduces local refinement of flat‐top partition of unity mesh within the framework of high‐order approximation in one‐ and two‐dimensional spaces, respectively. Based on the traditional PU mesh, the construction of locally refined flat‐top PU mesh is straightforward. With the rank deficiency counting approach, linear independence is proven from element level for the locally refined mesh system. Based on the numerical solution procedure presented, two numerical examples are analyzed to verify the proposed approximation method.||URI:||https://hdl.handle.net/10356/137137||ISSN:||0029-5981||DOI:||10.1002/nme.5932||Rights:||© 2018 John Wiley & Sons Ltd. All rights reserved. This paper was published in International Journal for Numerical Methods in Engineering and is made available with permission of John Wiley & Sons Ltd.||Fulltext Permission:||open||Fulltext Availability:||With Fulltext|
|Appears in Collections:||CEE Journal Articles|
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