Analysis of contact problems of porous thermoelastic solids

In this article, we study a contact problem between a one-dimensional porous
thermoelastic layer and a rigid obstacle. The mechanical problem consists of a
coupled system of two hyperbolic partial differential equations and a parabolic
one. By defining penalized problems, an energy decay property is obtained.
Then, fully discrete algorithms are introduced to approximate both penalized
and Signorini problems using the nite element method and the implicit
Euler scheme. Stability properties are shown for both problems and a priori
error estimates are proved for the penalized problem, from which the linear
convergence of the algorithm is derived. Finally, some numerical simulations
are performed to demonstrate the accuracy of the approximation and the
behavior of the solution.