# Numerical analysis of a frictionless viscoelastic piezoelectric contact problem

Mikael Barboteu; Jose Ramon Fernández; Youssef Ouafik

ESAIM: Mathematical Modelling and Numerical Analysis (2008)

- Volume: 42, Issue: 4, page 667-682
- ISSN: 0764-583X

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topBarboteu, Mikael, Fernández, Jose Ramon, and Ouafik, Youssef. "Numerical analysis of a frictionless viscoelastic piezoelectric contact problem." ESAIM: Mathematical Modelling and Numerical Analysis 42.4 (2008): 667-682. <http://eudml.org/doc/250379>.

@article{Barboteu2008,

abstract = {
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.
},

author = {Barboteu, Mikael, Fernández, Jose Ramon, Ouafik, Youssef},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Piezoelectricity; viscoelasticity; normal compliance; error estimates;
numerical simulations.; existence; uniqueness; finite element method; Euler scheme},

language = {eng},

month = {6},

number = {4},

pages = {667-682},

publisher = {EDP Sciences},

title = {Numerical analysis of a frictionless viscoelastic piezoelectric contact problem},

url = {http://eudml.org/doc/250379},

volume = {42},

year = {2008},

}

TY - JOUR

AU - Barboteu, Mikael

AU - Fernández, Jose Ramon

AU - Ouafik, Youssef

TI - Numerical analysis of a frictionless viscoelastic piezoelectric contact problem

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2008/6//

PB - EDP Sciences

VL - 42

IS - 4

SP - 667

EP - 682

AB -
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.

LA - eng

KW - Piezoelectricity; viscoelasticity; normal compliance; error estimates;
numerical simulations.; existence; uniqueness; finite element method; Euler scheme

UR - http://eudml.org/doc/250379

ER -

## References

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