An adaptive finite element approach for frictionless contact problems

The derivation of an a posteriori error estimator for frictionless contact problems under the hypotheses of linear elastic behaviour and infinitesimal deformation is presented. The approximated solution of this problem is obtained by using the finite element method. A penalization or augmented‐Lagra...

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Bibliographic Details
Published in:International journal for numerical methods in engineering 2001-01, Vol.50 (2), p.395-418
Main Authors: Buscaglia, Gustavo C., Durán, Ricardo, Fancello, Eduardo A., Feijóo, Raúl A., Padra, Claudio
Format: Article
Language:English
Subjects:
adaptive analysis
error estimator
finite element method
frictionless contact problems
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Summary:The derivation of an a posteriori error estimator for frictionless contact problems under the hypotheses of linear elastic behaviour and infinitesimal deformation is presented. The approximated solution of this problem is obtained by using the finite element method. A penalization or augmented‐Lagrangian technique is used to deal with the unilateral boundary condition over the contact boundary. An a posteriori error estimator suitable for adaptive mesh refinement in this problem is proposed, together with its mathematical justification. Up to the present time, this mathematical proof is restricted to the penalization approach. Several numerical results are reported in order to corroborate the applicability of this estimator and to compare it with other a posteriori error estimators. Copyright © 2001 John Wiley & Sons, Ltd.
ISSN:0029-5981
1097-0207
DOI:10.1002/1097-0207(20010120)50:2<395::AID-NME30>3.0.CO;2-#