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Conservation properties of a time FE method. IV: Higher order energy and momentum conserving schemes. (English) Zbl 1134.74406

Summary: In the present paper a systematic development of higher order accurate time stepping schemes which exactly conserve total energy as well as momentum maps of underlying finite-dimensional Hamiltonian systems with symmetry is shown. The result of this development is the enhanced Galerkin (eG) finite element method in time. The conservation of the eG method is generally related to its collocation property. Total energy conservation, in particular, is obtained by a new projection technique. The eG method is, moreover, based on objective time discretization of the used strain measure. This paper is concerned with particle dynamics and semi-discrete non-linear elastodynamics. The related numerical examples show good performance in presence of stiffness as well as for calculating large-strain motions.
[For part I, cf. Int. J. Numer. Methods Eng. 49, No.5, 599–638 (2000; Zbl 0964.70002); for part II, cf. ibid. 50, No. 8, 1931–1955 (2001; Zbl 1134.74402); for part III, cf. ibid. 53, No. 10, 2271–2304 (2002; Zbl 1134.70300).]

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74H15 Numerical approximation of solutions of dynamical problems in solid mechanics
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