Semi-Discrete and Fully Discrete Partial Projection Finite Element Methods for the Vibrating Timoshenko Beam

Abstract

In this paper, the partial projection finite element method is applied to the time-dependent problem – the damped vibrating Timoshenko beam model. It is proved that this method allows some new combinations of interpolations for stress and displacement fields. When assuming that a smooth solution exists, we obtain optimal convergence rates with constants independent of the beam thickness.