Timoshenko's problem

Timoshenko's problem is not a recent problem and many articles exist concerning his study.  New physical problems appear and require a good mathematical understanding of the behavior of this phenomenon.  Our contribution will consist in studying the numerical stability of a Timoshenko system with second sound.  We introduce a finite element approximation and prove that the associated discrete energy decreases and we establish a priori error estimates.  Finally, some numerical simulations are obtained.