Convergence of AVI’s for the linear elastodynamics of simple bodies

Asynchronous variational integrators (AVIs) are a class of algorithms that allow to discretize continuous models of evolutionary phenomena and preserve their simplectic structure, when it is present. When the phenomenon under analysis is composed by subsystems, AVIs allow one to attribute to each subsystem different time discretizations in a way useful to assure that the energy is “nearly” preserved along computations in the conservative case. Here we summarize a new proof of the convergence of AVIs in the case of linear elastodynamics.