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.
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