C1-continuous space-time discretization based on Hamilton's law of varying action

@article{Mergel2015C1continuousSD,
  title={C1-continuous space-time discretization based on Hamilton's law of varying action},
  author={Janine C. Mergel and R. Sauer and S. Ober-Bl{\"o}baum},
  journal={ArXiv},
  year={2015},
  volume={abs/1510.07863}
}
  • Janine C. Mergel, R. Sauer, S. Ober-Blöbaum
  • Published 2015
  • Mathematics, Computer Science
  • ArXiv
  • We develop a class of C1-continuous time integration methods that are applicable to conservative problems in elastodynamics. These methods are based on Hamilton's law of varying action. From the action of the continuous system we derive a spatially and temporally weak form of the governing equilibrium equations. This expression is first discretized in space, considering standard finite elements. The resulting system is then discretized in time, approximating the displacement by piecewise cubic… CONTINUE READING

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 109 REFERENCES
    Conservation properties of a time FE method—part II: Time-stepping schemes for non-linear elastodynamics
    131
    Time Finite Element Discretization of Hamilton's Law of Varying Action
    43
    Discontinuous variational time integrators for complex multibody collisions
    9
    Variational time integrators
    244
    Geometric discretization of nonholonomic systems with symmetries
    42
    Variational integrators for constrained dynamical systems
    129