On the mixtures of MGT viscoelastic solids

In this paper, we study, from both analytical and numerical points of view, a problem in-volving a mixture of two viscoelastic solids. An existence and uniqueness result is proved using the theory of linear semigroups. Exponential decay is shown for the one-dimensional case. Then, fully discrete approximations are introduced using the finite element method and the implicit Euler scheme. Some a priori error estimates are obtained and the linear convergence is derived under suitable regular-ity conditions. Finally, one-and two-dimensional numerical simulations are presented to demonstrate the convergence, the discrete energy decay and the behavior of the solution.