Analysis of a contact problem for a viscoelastic Bresse system

In this paper, we consider a contact problem between viscoelastic Bresse beam and deformable obstacle. The well-known normal compliance condition is used to model the contact. existence of unique solution continuous proved using Faedo-Galerkin method. An exponential decay property also obtained defining an adequate Liapunov function. Then, finite element method implicit Euler scheme, approximation introduced. A discrete stability priori error estimates are proved. Finally, some numerical experiments performed demonstrate energy convergence.