Finite Element Error Analysis of a Viscoelastic Timoshenko Beam with Thermodiffusion Effects

In this paper, a thermomechanical problem involving viscoelastic Timoshenko beam is analyzed from numerical point of view. The so-called thermodiffusion effects are also included in the model. written as linear system composed two second-order-in-time partial differential equations for transverse displacement and rotational movement, first-order-in-time temperature chemical potential. corresponding variational formulation leads to coupled first-order terms velocity, rotation speed, existence uniqueness solutions, well energy decay property, stated. Then, we focus on approximation weak by using implicit Euler scheme discretize time derivatives classical finite element method approximate spatial variable. A discrete stability property some priori error estimates shown, which can conclude convergence approximations under suitable additional regularity conditions. Finally, simulations performed demonstrate accuracy scheme, behavior dependence solution with respect parameters.