  The notions of discrete conformality on triangle meshes have rich
mathematical theories and wide applications. The related notions of discrete
uniformizations on triangle meshes, suggest efficient methods for computing the
uniformizations of surfaces. This paper proves that the discrete
uniformizations approximate the continuous uniformization for closed surfaces
of genus $\geq1$, when the approximating triangle meshes are reasonably good.
To the best of the authors' knowledge, this is the first convergence result on
computing uniformizations for surfaces of genus $>1$.
