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On the construction of blending elements for local partition of unity enriched finite elements
Author(s) -
Chessa Jack,
Wang Hongwu,
Belytschko Ted
Publication year - 2003
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.777
Subject(s) - partition of unity , partition (number theory) , finite element method , convergence (economics) , rate of convergence , mathematics , polynomial , element (criminal law) , mathematical optimization , function (biology) , mathematical analysis , computer science , engineering , combinatorics , structural engineering , computer network , channel (broadcasting) , evolutionary biology , law , political science , economics , biology , economic growth
For computational efficiency, partition of unity enrichments are preferably localized to the sub‐domains where they are needed. It is shown that an appropriate construction of the elements in the blending area, the region where the enriched elements blend to unenriched elements, is often crucial for good performance of local partition of unity enrichments. An enhanced strain formulation is developed which leads to good performance; the optimal rate of convergence is achieved. For polynomial enrichments, it is shown that a proper choice of the finite element shape functions and partition of unity shape functions also improves the accuracy and convergence. The methods are illustrated by several examples. The examples deal primarily with the signed distance function enrichment for treating discontinuous derivatives inside an element, but other enrichments are also considered. Results show that both methods provide optimal rates of convergence. Copyright © 2003 John Wiley & Sons, Ltd.