The purpose of this paper is to survey some recent advances in variational integrators for
both finite dimensional mechanical systems as well as continuum mechanics. These …

The paper provides an introduction and survey of conservative discretization methods for
Hamiltonian partial differential equations. The emphasis is on variational, symplectic and …

In this paper we discuss energy conservation issues related to the numerical solution of the
semilinear wave equation. As is well known, this problem can be cast as a Hamiltonian …

Variational integrators are a class of discretizations for mechanical systems which are
derived by discretizing Hamilton's principle of stationary action. They are applicable to both …

Geometric mechanics involves the study of Lagrangian and Hamiltonian mechanics using
geometric and symmetry techniques. Computational algorithms obtained from a discrete …

Hamiltonian PDEs have some invariant quantities, which would be good to conserve with
the numerical integration. In this paper, we concentrate on the nonlinear wave and …

In this paper, we develop a structure-preserving discretization of the Lagrangian framework
for electrodynamics, combining the techniques of variational integrators and discrete …

The numerical analysis of variational integrators relies on variational error analysis, which
relates the order of accuracy of a variational integrator with the order of approximation of the …

The coupled sine-Gordon (SG) equations and the coupled Klein-Gordon (KG) equations
play an important role in scientific fields, such as nonlinear optics, solid state physics …

The coupled motion between shallow-water sloshing in a moving vehicle and the vehicle
dynamics is considered, with the vehicle dynamics restricted to horizontal motion. The paper …