title: Higher order temporal finite element methods through mixed formalisms.
abstract: The extended framework of Hamilton's principle and the mixed convolved action principle provide new rigorous weak variational formalism for a broad range of initial boundary value problems in mathematical physics and mechanics. 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 symplectic and unconditionally stable with respect to the time step. For the damped system, they are shown to be accurate with good convergence characteristics.
authors.affiliation: School of Civil, Environmental and Architectural Engineering, Korea University, Anam-dong5-ga1, Seongbuk-goo, 136-713 South Korea.
authors.forename: Jinkyu
authors.initials: J
authors.lastname: Kim
keywords: Higher order methods; Initial value problems; Mixed formulation; Temporal finite element method; Variational formalism