  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.
