Analysis of a contact problem involving thermoelastic mixtures

In this work we study a dynamic contact problem between a thermoelastic mixture and a deformable obstacle. The classical normal compliance condition is used for modeling the contact. The variational formulation of this problem is written as a nonlinear coupled system of three parabolic variational equations. An existence and uniqueness result is proved using the Faedo-Galerkin method. Then, fully discrete approximations are introduced by using the finite element method and the implicit Euler scheme. A discrete stability property and a priori error estimates are proved, from which the decay of the discrete energy and the linear convergence of the algorithm are deduced. Finally, some numerical simulations are presented to show the convergence and the behavior of the solution