Abstract: In this talk, we talk about error estimates for Alexandrov’s solutions to the Dirichlet
problem of the Monge-Ampere equation $\det D^2 u=f$ in $\Omega$, where $f$ is a positive
and continuous function and $\Omega$ is a bounded convex domain in the Euclidean space
$R^n$. We approximate the solution $u$ by a sequence of convex polyhedra $v_h$, which
are generalised solutions to the Monge-Amp\`ere equation in the sense of Aleksandrov, and
the associated Monge-Amp\`ere measures $\nu_h$ are supported on a properly chosen grid
in $\Omega$. We will derive error estimates for the cases when $f$ is smooth, H\"older
continuous, and merely continuous. This is a joint work with Haodi Chen and Xu-Jia Wang.