Error analysis of variational integrators of unconstrained Lagrangian systems

TL;DR

This paper provides a comprehensive error analysis of variational integrators for unconstrained Lagrangian systems, revealing a singularity issue at zero time-step and proposing a symmetry-based correction to match observed simulation accuracy.

Contribution

It introduces a novel error analysis approach by addressing singularities in discrete variational principles and proposes a symmetry correction to improve accuracy.

Findings

Error analysis shows a one-order deficit due to singularities

A new past-future symmetry corrects the order discrepancy

Analysis aligns theoretical predictions with simulation results

Abstract

A complete error analysis of variational integrators is obtained, by blowing up the discrete variational principles, all of which have a singularity at zero time-step. Divisions by the time step lead to an order that is one less than observed in simulations, a deficit that is repaired with the help of a new past-future symmetry.