Discrete models of coupled dynamic thermoelasticity for stress-temperature formulations

In this article, the author studies the properties of discrete approximations for mathematical models of coupled thermoelasticity in the stress-temperature formulation. Since many applied problems deal with steep gradients of thermal elds, the main emphasis is given to the investigation of non-smooth solutions of non-stationary thermoelasticity. Convergence of operator-diierence schemes on weak solutions of thermoelasticity is proved, and the dispersion analysis of models is performed. Error estimates and the results of computational experiments are presented. In essence, any mathematical model describes a transformation of diierent types of energy. The recognition of this fact leads to an integral reformulation of diierential models. On the one hand, such a reformulation is a fundamental step in obtaining eeective numerical procedures of projective-variational type. On the other hand, such a reformulation allows us to relax the theoretical assumptions about a solution's smoothness typically made for diierential problems. In the nal analysis, we do not know a priori regularity of the solution when solving a practical problem. Hence it is always necessary to cover a gap between mathematical assumptions on the solution smoothness and the smoothness of the solution in a real problem. Properly organized computational experiments may not only verify the validity of theoretical assumptions and estimates, but also identify new eeects and tendencies that may lead to new directions A part of this work was presented by the author at the Xth International Conference \Numerical Methods for Thermal Problems" that took place at the University of Wales Swansea, U.K. in July 1997.