First variation formula for discrete variational problems in two independent variables (Q1935053)

The authors introduce a geometric setup for discrete variational problems in two independent variables, which is based on the theory of bundles modelled on cell complexes. Using this approach, geometrical characterizations of the first variation formula (see Theorem 2) and the Discrete Noether theorem (see Theorem 4) are given. Finally, the existence of some discrete variational integrators is investigated (see Section 4) and the theory is illustrated by an example concerning a variational integrator for the movement of a string.