Numerical studies of a Timoshenko system with the second sound

Source abstract

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.