Euler-Poincare reduction for discrete field theories

Abstract

In this note, we develop a theory of Euler-Poincare reduction for discrete Lagrangian field theories. We introduce the concept of Euler-Poincare equations for discrete field theories, as well as a natural extension of the Moser-Veselov scheme, and show that both are equivalent. The resulting discrete field equations are interpreted in terms of discrete differential geometry. An application to the theory of discrete harmonic mappings is also briefly discussed.

arXiv comment24 pages, 3 figures (v2: simplified treatment)

References in corpus (6)

• Multisymplectic geometry, variational integrators, and nonlinear PDEs
• Discrete Euler-Poincaré and Lie-Poisson Equations
• Discrete time Lagrangian mechanics on Lie groups, with an application to the Lagrange top
• Discrete Lagrangian and Hamiltonian Mechanics on Lie groupoids
• Symmetries in Classical Field Theory
• Discrete Lagrangian field theories on Lie groupoids

Cited by in corpus (8)

• Reduction of polysymplectic manifolds
• K-symplectic formalism on Lie algebroids
• Remarks on multisymplectic reduction
• Discrete Dirac reduction of implicit Lagrangian systems with abelian symmetry groups
• Geometry of discrete-time spin systems
• Symmetry reduction, integrability and reconstruction in k-symplectic field theory
• Discrete Formulation for the dynamics of rods deforming in space
• Gauge reduction in covariant field theory