In this work, we consider the quasistatic frictionless contact problem between a viscoelastic piezoelectric body and a deformable obstacle. The linear electro-viscoelastic constitutive law is employed to model the piezoelectric material and the normal compliance condition is used to model the contact. The variational formulation is derived in a form of a coupled system for the displacement and electric potential fields. An existence and uniqueness result is recalled. Then, a fully discrete scheme is introduced based on the finite element method to approximate the spatial variable and an Euler scheme to discretize the time derivatives. Error estimates are derived on the approximative solutions and, as a consequence, the linear convergence of the algorithm is deduced under suitable regularity conditions. Finally, some two-dimensional examples are presented to demonstrate the performance of the algorithm.
@article{M2AN_2008__42_4_667_0,
author = {Barboteu, Mikael and Fern\'andez, Jose Ramon and Ouafik, Youssef},
title = {Numerical analysis of a frictionless viscoelastic piezoelectric contact problem},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {42},
year = {2008},
pages = {667-682},
doi = {10.1051/m2an:2008022},
mrnumber = {2437778},
zbl = {1142.74029},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2008__42_4_667_0}
}
Barboteu, Mikael; Fernández, Jose Ramon; Ouafik, Youssef. Numerical analysis of a frictionless viscoelastic piezoelectric contact problem. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 42 (2008) pp. 667-682. doi : 10.1051/m2an:2008022. http://gdmltest.u-ga.fr/item/M2AN_2008__42_4_667_0/
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