Analysis and performance of a predictor-multicorrector Time Discontinuous Galerkin method in non-linear elastodynamics

A predictor-multicorrector implementation of a Time Discontinuous Galerkin method for non-linear dynamic analysis is described. This implementation is intended to limit the high computational expense typically required by implicit Time Discontinuous Galerkin methods, without degrading their accuracy and stability properties. The algorithm is analysed with reference to conservative Duffing oscillators for which closed-form solutions are available. Therefore, insight into the accuracy and stability properties of the predictor-multicorrector algorithm for different approximations of non-linear internal forces is gained, showing that the properties of the underlying scheme can be substantially retained. Finally, the results of representative numerical simulations relevant to Duffing oscillators and to a stiff spring pendulum discretized with finite elements illustrate the performance of the numerical scheme and confirm the analytical estimates. Copyright