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The EHP and the MCAP provide new rigorous weak variational formalism for abroad range of initial boundary value problems in mathematical physics andmechanics. Both approaches utilize the mixed formulation and lead to thedevelopment of various space-time finite element methods. In this paper, theirpotential when adopting temporally higher order approximations is investigated.The classical single-degree-of-freedom dynamical systems are primarilyconsidered to validate and to investigate the performance of the numericalalgorithms developed from both formulations. For the undamped system, all thealgorithms are found to be symplectic and unconditionally stable with respectto the time step. On the other hand, for the damped system, the approach isshown to be robust and to be accurate with good convergence characteristics.

Higher order temporal finite element methods through mixed formulations