Comparison of Different Error Indicators for Contact Problems Involving Large Elastic Strains

authored by: A. Rieger, Peter Wriggers
Abstract: Finite element methods (FEMs) are flexible tools which can be applied to solve contact problems with arbitrary geometries. As in any numerical method, the solutions obtained with FEM are only approximate. Errors occur e.g. due to the choice of the ansatz space and the approximation of the geometry. In general it is necessary to automatically control the error inherited in the method to obtain reliable solutions. This is especially true in case of non-linear contact problems since geometry and contact surface can change substantially during the deformation process. Thus the refinement process needed for an accurate analysis cannot be controlled by the user beforehand. Here an adaptive FEM is developed for large strain problems of two or more deformable bodies being in contact. The main focus is the comparison of different error indicators and error estimators related to the contact problem. In detail residual based, error estimators, error indicators relying on superconvergence properties and error estimators based on duality principles are investigated. Finally, examples show the convergence behaviour of the error measures.
Organisation(s): Institute of Mechanics and Computational Mechanics
Type: Article
Journal: International Journal of Phytoremediation
Volume: 21
Pages: 575-601
No. of pages: 27
ISSN: 1522-6514
Publication date: 2003
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Environmental Chemistry, Pollution, Plant Science
Electronic version(s): https://doi.org/10.1080/0003681031000112185 (Access: Unknown)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{f8ff921d66fe4646ac049e944e623c66,
title = "Comparison of Different Error Indicators for Contact Problems Involving Large Elastic Strains",
abstract = "Finite element methods (FEMs) are flexible tools which can be applied to solve contact problems with arbitrary geometries. As in any numerical method, the solutions obtained with FEM are only approximate. Errors occur e.g. due to the choice of the ansatz space and the approximation of the geometry. In general it is necessary to automatically control the error inherited in the method to obtain reliable solutions. This is especially true in case of non-linear contact problems since geometry and contact surface can change substantially during the deformation process. Thus the refinement process needed for an accurate analysis cannot be controlled by the user beforehand. Here an adaptive FEM is developed for large strain problems of two or more deformable bodies being in contact. The main focus is the comparison of different error indicators and error estimators related to the contact problem. In detail residual based, error estimators, error indicators relying on superconvergence properties and error estimators based on duality principles are investigated. Finally, examples show the convergence behaviour of the error measures.",
author = "A. Rieger and Peter Wriggers",
year = "2003",
doi = "10.1080/0003681031000112185",
language = "English",
volume = "21",
pages = "575--601",
journal = "International Journal of Phytoremediation",
issn = "1522-6514",
publisher = "Taylor and Francis Ltd.",
number = "1",
}