On the numerical approximation of a problem involving a mixture of a MGT viscous material and an elastic solid

In this work, we analyze, from the numerical point of view, a problem including mixture made MGT viscoelastic solid and an elastic solid. The corresponding variational is linear system composed two coupled hyperbolic equations written in terms acceleration first constituent velocity second one. Then, fully discrete approximations are introduced by using finite element method implicit Euler scheme. A stability property priori error estimates proved. Finally, some one-dimensional simulations shown to demonstrate accuracy proposed behaviour solution.