Time-discontinuous stabilized space-time finite elements for Timoshenko beams

Stabilized space-time finite element methods for the transient computationa l analysis of the elastodynamics of Timoshenko beams have been developed. T he underlying time-discontinuous Galerkin formulation is implicit, uncondit ionally stable, higher-order accurate, and robust. The employed interpolati ons are continuous in space and time inside time slabs, but discontinuous i n time between adjacent time slabs. To suppress spurious numerical oscillat ions near discontinuities or high gradients, Galerkin/least-squares stabili zation has been applied. Further improvement of the numerical representatio n of the transient elastic wave propagation phenomena has been achieved by specially designed Galerkin/gradient least-squares operators. Because of th e reduced phase and amplitude errors of these finite elements, much coarser spatial meshes may be used without loss of accuracy. The resulting reducti on of the number of unknowns leads to a significant decrease of computer ti me. Furthermore, a global adaptive time-stepping strategy has been employed based on the temporal jump residual of the time finite element method as e rror estimator. Numerical examples of transient elastic wave propagation in Timoshenko beams involving a wide spectrum of wave numbers and frequencies demonstrate the good performance of the developed methods.