A numerical study of swelling porous thermoelastic media with second sound

In this work, we numerically consider a swelling porous thermoelastic system with a heat flux given by the Maxwell–Cattaneo law.  We study the numerical energy and the exponential decay of the thermoelastic problem.  First, we give a variational formulation written in terms of the transformed derivatives corresponding to a coupled linear system composed of four first-order variational equations.  A fully discrete algorithm is introduced and a discrete stability property is proven.  A priori error estimates are also provided.  Finally, some numerical results are given to demonstrate the behavior of the solution.