Steklov's Operator Technique in Coupled Dynamic Thermoelasticity

In this paper we study non-smooth solutions of coupled non-stationary problems in thermoelasticity. Since the classical tools based on the Tay-lor's expansion of unknown functions may not be appropriate in obtaining a measure of quality for numerical methods, we apply the averaging Steklov operators and the technique based on the Bramble-Hilbert lemma in order to establish the convergence result for a class of generalized solutions. EEective explicit numerical schemes and error estimates are presented. 1 Coupled Field Theory and Hyperbolic Modes in Dynamics. All real processes, dynamic systems and phenomena describe a transformation of diierent types of energy. This implies that in general, mathematical models applied to them should have integral rather than diierential features. However, when engaged in mathematical modelling, we can often observe a gap between theoretical assumptions about a solution's smoothness and the actual smoothness of the solution in a practical problem. Moreover, including additional information about the process, system or phenomenon into the model (for example, by an improved physical parameterization or by additional relations between system parameters) ultimately leads to a change of solution regularity. The process of model improvement may continue in-deenitely, and hence it is important to nd a balance between the energetic and informational parts of the model complexity 23, 14]. Coupling, which is a natural way of reeecting additional information about a process, system,