Volume 55, Number 3, May-June 2021
|Page(s)||887 - 911|
|Published online||05 May 2021|
Analysis of a contact problem for a viscoelastic Bresse system
LANA, Departamento de Matemática, Universidade Federal de Santa Maria, 97105-900 Santa Maria, RS, Brazil
2 Department of Mathematics and Computer Science, Faculty of Science, Beirut Arab University, Debbieh, Lebanon
3 Departamento de Matemática Aplicada I, Universidade de Vigo, Escola de Enxeñería de Telecomunicación, Campus As Lagoas Marcosende s/n, 36310 Vigo, Spain
4 Dipartimento di Ingegneria Civile, Architettura, Territorio, Ambiente e di Matematica, Università degli Studi di Brescia, Via Valotti 9, 25133 Brescia, Italy
5 Department of Mathematics, Faculty of Sciences 1, Lebanese University, Hadath, Lebanon
* Corresponding author: firstname.lastname@example.org
Accepted: 22 March 2021
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.
Mathematics Subject Classification: 65M15 / 65M60 / 74B05 / 74K10
Key words: Contact problem / Bresse beam / exponential decay / finite element discretization
© EDP Sciences, SMAI 2021
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