An a priori error analysis of poro-thermoviscoelastic problems

Abstract

In this paper, we study, from the numerical point of view, a dynamic one-dimensional problem arising in thermoelasticity and thermoviscoelasticity of types II and III. Porosity is also included into the models. The generic variational formulation leads to a coupled system written in terms of the velocity, the volume fraction speed and the temperature. Fully discrete approximations are then introduced by using the finite element method and the implicit Euler scheme. A discrete stability property and a priori error estimates are proved. Finally, some numerical examples are presented to demonstrate the numerical convergence of the algorithm, the exponential decay of the discrete energy and the behavior of the solution