Rate of convergence of difference approximations for uniformly nondegenerate elliptic Bellman's equations

TL;DR

This paper establishes that finite-difference solutions for uniformly elliptic Bellman's equations in smooth domains converge at a rate of at least h^{2/3}, providing a quantitative measure of approximation accuracy.

Contribution

It proves a new lower bound on the convergence rate of finite-difference schemes for elliptic Bellman's equations in smooth bounded domains.

Findings

Convergence rate is at least h^{2/3} for finite-difference solutions.

Results apply to uniformly elliptic Bellman's equations in smooth domains.

Provides theoretical foundation for numerical approximation accuracy.

Abstract

We show that the rate of convergence of solutions of finite-difference approximations for uniformly elliptic Bellman's equations is of order at least $h^{2/3}$, where $h$ is the mesh size. The equations are considered in smooth bounded domains.