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High-order finite elements compared to low-order mixed element formulations
Publikationstyp
Journal Article
Date Issued
2012-09-24
Sprache
English
Author(s)
TORE-URI
Journal
Volume
93
Issue
2-3
Start Page
163
End Page
176
Citation
ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik 2-3 (93): 163-176 (2013)
Publisher DOI
Scopus ID
Publisher
Wiley-VCH
High-order finite elements are commonly compared with linear element formulations showing that, in terms of the relation between computational time and achievable accuracy, linear element formulations are inferior to high-order elements. On the other hthe finite element community follows the h-version approach due to its simplicity in implementation. This article compares high-order finite elements based on hierarchic shape functions with low-order mixed element formulations using finite strain hyperelasticity. These comparisons are conducted from the point of view of both accuracy and efficiency as well as highly deformed structures. It also investigates improvements to minimize the overall computational effort such as parallelizing the element assemblage procedure, choosing a starting vector estimator for Newton's method, and investigating the Newton-Chord method. The advantages and disadvantages of both finite element approaches are also discussed. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Subjects
Finite elements
Finite strains
Hierarchic shape functions
Hyperelasticity
Mixed elements.
DDC Class
510: Mathematik
More Funding Information
Deutsche Forschungsgemeinschaft (DFG); grant numbers HA 2024/7-1 and DU 405/3-1