Mixed finite element formulations in the time domain for solution of dynamic problems

This paper presents a two-field mixed finite element formulation in the time domain. Several strategies are presented by which the variational formulations are produced. One strategy is based on Hamilton's law, and is suitable for problems where the mechanical energy of the system is given. Another strategy uses the Galerkin method, which is suitable when the equations of motion are given. This strategy can either be based on a continuous or discontinuous approximation of the physical variables in time. All formulations were analyzed, and their characteristics in terms of truncation error (phase and amplitude) and stability are presented. This analysis was verified by numerical results. Comparison of many formulations leads to the conclusion that discontinuous mixed finite element method in the time domain is superior to all others in terms of stability and accuracy.