# A sharp error analysis for the discontinuous Galerkin method of optimal control problems

## TL;DR

This paper provides precise error estimates for the discontinuous Galerkin method applied to nonlinear optimal control problems governed by ordinary differential equations, supported by numerical validation.

## Contribution

It offers sharp error bounds for the DG method of arbitrary order in nonlinear optimal control, under regularity assumptions, advancing the theoretical understanding of discretization accuracy.

## Key findings

- Sharp error estimates for the DG method of arbitrary order
- Numerical experiments confirm theoretical error bounds
- Enhanced understanding of discretization errors in optimal control

## Abstract

In this paper, we are concerned with a nonlinear optimal control problem of ordinary differential equations. We consider a discretization of the problem with the discontinuous Galerkin method with arbitrary order $r \in \mathbb{N}\cup \{0\}$. Under suitable regularity assumptions on the cost functional and solutions of the state equations, we provide sharp estimates for the error of the approximate solutions. Numerical experiments are presented supporting the theoretical results.