In this paper, we consider a contact problem between a viscoelastic Bresse beam and a deformable obstacle. The well-known normal compliance contact condition is used to model the contact. The existence of a unique solution to the continuous problem is proved using the Faedo-Galerkin method. An exponential decay property is also obtained defining an adequate Liapunov function. Then, using the finite element method and the implicit Euler scheme, a finite element approximation is introduced. A discrete stability property and a priori error estimates are proved. Finally, some numerical experiments are performed to demonstrate the decay of the discrete energy and the numerical convergence.
Accepté le :
Publié le :
DOI : 10.1051/m2an/2021015
Keywords: Contact problem, Bresse beam, exponential decay, finite element discretization
@article{M2AN_2021__55_3_887_0,
author = {Copetti, Maria In\^es M. and EL Arwadi, Toufic and Fern\'andez, Jose R. and Naso, Maria Grazia and Youssef, Wael},
title = {Analysis of a contact problem for a viscoelastic {Bresse} system},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {887--911},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {3},
doi = {10.1051/m2an/2021015},
mrnumber = {4253165},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2021015/}
}
TY - JOUR AU - Copetti, Maria Inês M. AU - EL Arwadi, Toufic AU - Fernández, Jose R. AU - Naso, Maria Grazia AU - Youssef, Wael TI - Analysis of a contact problem for a viscoelastic Bresse system JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2021 SP - 887 EP - 911 VL - 55 IS - 3 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2021015/ DO - 10.1051/m2an/2021015 LA - en ID - M2AN_2021__55_3_887_0 ER -
%0 Journal Article %A Copetti, Maria Inês M. %A EL Arwadi, Toufic %A Fernández, Jose R. %A Naso, Maria Grazia %A Youssef, Wael %T Analysis of a contact problem for a viscoelastic Bresse system %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2021 %P 887-911 %V 55 %N 3 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2021015/ %R 10.1051/m2an/2021015 %G en %F M2AN_2021__55_3_887_0
Copetti, Maria Inês M.; EL Arwadi, Toufic; Fernández, Jose R.; Naso, Maria Grazia; Youssef, Wael. Analysis of a contact problem for a viscoelastic Bresse system. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021) no. 3, pp. 887-911. doi: 10.1051/m2an/2021015
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