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On the approximate problem for the incremental thermoelasticity

Abstract In this work, we study an approximate problem arising in the incremental thermoelasticity. The existence of a unique solution is proved applying the theory of linear semigroups. The exponential energy decay is also considered. Then, fully discrete approximations are introduced using the finite element method and the implicit Euler scheme. A discrete stability property and a priori error estimates are shown. Finally, numerical simulations are presented to demonstrate the accuracy of the approximations and the behavior of the model. In view of our numerical results the approximate problem could be used only when a certain parameter is small if we compare it with other parameters arising in the problem.