# Convergence Rate for the Ordered Upwind Method

arXiv: https://arxiv.org/abs/1601.02885 · HTML: https://mlsanity.com/paper/1601.02885/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jan 2016.

## Built on by (most cited first, 1 of 1)

- [Controlling mean exit time of stochastic dynamical systems based on quasipotential and machine learning](https://mlsanity.com/paper/2209.13098/) (2022)

## Abstract (arXiv)

The Ordered Upwind Method (OUM) is used to approximate the viscosity solution of the static Hamilton-Jacobi-Bellman (HJB) with direction-dependent weights on unstructured meshes. The method has been previously shown to provide a solution that converges to the exact solution, but no convergence rate has been theoretically proven. In this paper, it is shown that the solutions produced by the OUM in the boundary value formulation converge at a rate of at least the square root of the largest edge length in the mesh in terms of maximum error. An example with similar order of numerical convergence is provided.