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Higher order temporal finite element methods through mixed formulations

The EHP and the MCAP provide new rigorous weak variational formalism for a broad range of initial boundary value problems in mathematical physics and mechanics. Both approaches utilize the mixed formulation and lead to the development of various space-time finite element methods. In this paper, their potential when adopting temporally higher order approximations is investigated. The classical single-degree-of-freedom dynamical systems are primarily considered to validate and to investigate the performance of the numerical algorithms developed from both formulations. For the undamped system, all the algorithms are found to be symplectic and unconditionally stable with respect to the time step. On the other hand, for the damped system, the approach is shown to be robust and to be accurate with good convergence characteristics.