An a priori error analysis of swelling porous thermoelastic soils mixture with second sound

Abstract

This paper presents a numerical investigation of a one-dimensional swelling porous thermoelastic system modeling a soil mixture subjected to heat flux governed by the Maxwell–Cattaneo law. We focus on the analysis of the discrete energy and the exponential decay properties of the associated thermoelastic problem. A variational formulation is introduced, leading to a coupled linear system of four first-order equations. Based on this formulation, a fully discrete numerical scheme is developed and its discrete stability is rigorously established. Furthermore, a priori error estimates are derived to quantify the accuracy of the proposed method. Numerical experiments are finally presented to illustrate the dynamical behavior of the solution and to confirm the theoretical stability and convergence results.