A Dynamic Thermoviscoelastic Problem: Numerical Analysis and Computational Experiments

In this paper, we consider the numerical analysis of a dynamic problem which models the temperature evolution in a thermoviscoelastic body. The variational problem is formulated as a coupled system of evolutionary nonlinear variational equations. An existence and uniqueness result is recalled. Then, a fully discrete numerical scheme is introduced by using the finite-element method to approximate the spatial variable and an Euler scheme to discretise the time derivatives. Error estimates are derived and, under suitable regularity assumptions, the linear convergence of the numerical scheme is obtained. Finally, the results of simulations of some two-dimensional numerical examples are presented to demonstrate the accuracy of the algorithm and the behaviour of the solution.