Convergence of a Numerical Scheme for the Hamilton-Jacobi Equation: a New Approach with the Adjoint Method

TL;DR

This paper introduces a new proof technique using the adjoint method to establish the convergence rate of a numerical scheme for the one-dimensional time-dependent Hamilton-Jacobi equation in a periodic setting.

Contribution

It provides a novel and simplified proof of convergence rates for a numerical scheme using the adjoint method, enhancing theoretical understanding.

Findings

Established convergence rate for the scheme

Simplified proof using the adjoint method

Applicable to periodic Hamilton-Jacobi equations

Abstract

We consider a numerical scheme for the one dimensional time dependent Hamilton-Jacobi equation in the periodic setting. We present a new and simple proof of the rate of convergence of the approximations based on the adjoint method recently introduced by Evans.