A porous thermoelastic problem: An a priori error analysis and computational experiments

In this paper, a porous thermoelastic problem is numerically considered. The variational formulation is written as a coupled system of two hyperbolic equations for the displacement and the porosity fields and a parabolic equation for the temperature field. An existence and uniqueness result as well as an energy decay property are recalled. Then, fully discrete approximations are introduced by using the finite element method to approximate the spatial variable and the backward Euler scheme to discretize the first-order time derivatives. A priori error estimates are proved, from which the linear convergence is deduced under some additional regularity conditions. Finally, some one- and two-dimensional numerical simulations are presented to show the accuracy of the approximation and the behavior of the solution.