Steklov's Operator Technique in Coupled Dynamic Thermoelasticity

Melnik, R.V.N.

Numerical Methods in Thermal Problems, Vol. X, Eds. R.W.Lewis and J.T.Cross, Pineridge Press, UK,  ISBN 0-906674-89-1, 139--150, 1997

Abstract:

In this paper we study non-smooth solutions of coupled non-stationary problems in thermoelasticity. Since the classical tools based on the Taylor'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 solution of dynamic thermoelasticity. Finally, effective explicit numerical schemes and error estimated are presented.

Key words: thermomechanical coupling; Bramble-Hilbert lemma; operator-difference schemes; weak solutions in thermoelasticity; optimal error control; balance between a priori and a posteriori estimates; Sobolev functional classes; convergence; parabolic-elliptic coupling; energetic and informational parts of model complexity.