Exponential stability of a fully discrete energy associated to a thermoviscoelastic Timoshenko system

This study concentrates on the mathematical analysis of a Timoshenko system incorporating Type III thermoelasticity and Kelvin-Voigt damping. Semigroup theory is employed to prove the well-posedness of the continuous system, and the exponential decay of the continuous energy is obtained. Later, a fully discrete numerical scheme is introduced. Particular attention is paid to the exponential decay of discrete energy. The Efficiency of the Proposed Numerical Scheme and the analysis of the decay of the discrete energy are justified by some numerical investigations.