Time finite element methods for structural dynamics

Abstract Time finite element methods are developed for the equations of structural dynamics. The approach employs the time‐discontinuous Galerkin method and incorporates stabilizing terms having least‐squares form. These enable a general convergence theorem to be proved in a norm stronger than the energy norm. Results are presented from finite difference analyses of the time‐discontinuous Galerkin and least‐squares methods with various temporal interpolations and commonly used finite difference methods for structural dynamics. These results show that, for particular interpolations, the time finite element method exhibits improved accuracy and stability.