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On convergence of the penalty method for a static unilateral contact problem with nonlocal friction in electro-elasticity

Published online by Cambridge University Press:  04 June 2015

El-H. BENKHIRA ,
El-H. ESSOUFI  and
R. FAKHAR
El-H. BENKHIRA
Affiliation:
University Moulay Ismaïl, ESTM, Laboratory LEM2A, BP 3103, Toulal-Meknès, Morocco email: benkhirahassan@yahoo.fr
El-H. ESSOUFI
Affiliation:
Univ Hassan 1, Laboratory MISI, 26000 Settat, Morocco email: e.h.essoufi@gmail.com
R. FAKHAR
Affiliation:
Univ Hassan 1, Laboratory LS3M, 25000 Settat, Morocco email: rachidfakhar@yahoo.fr
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Abstract

In this paper, we consider the penalty method to solve the unilateral contact with friction between an electro-elastic body and a conductive foundation. Mathematical properties, such as the existence of a solution to the penalty problem and its convergence to the solution of the original problem, are reported. Then, we present a finite elements approximation for the penalised problem and prove its convergence. Finally, we propose an iterative method to solve the resulting finite element system and establish its convergence.

Keywords

PiezoelectricVariational inequalityStatic friction contactNonlocal frictionSignorini conditionPenalty methodFixed point processFinite element approximation
Type
Papers
Information
European Journal of Applied Mathematics , Volume 27 , Issue 1 , February 2016 , pp. 1 - 22
Copyright
Copyright © Cambridge University Press 2015 

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