Huang, GenggengWang, Xu-Jia2021-06-162021-06-160036-1429http://hdl.handle.net/1885/237749In this paper, we establish convergence rate estimates for convex solutions to the Dirichlet problem of the Monge--Ampère equation det D^2u=f in Omega, where f is a positive and continuous function and Omega is a bounded convex domain in the Euclidean space mathbb{R}^n. We approximate the solution u by a sequence of convex polyhedra v_h, which are generalized solutions to the Monge--Ampère equation in the sense of Aleksandrov, and the associated Monge--Ampère measures nu_h are supported on a properly chosen grid in Omega. We will derive the convergence rate estimates for the cases when f is smooth, Hölder continuous, and merely continuous.This work was supported by ARC FL130100118 and DP170100929. The second author was also supported by NSFC11871160© 2019 Society for Industrial and Applied MathematicsMonge--Ampère equationconvergence rate estimate2019-01-2910.1137/18M1197217