Monge Ampere equation is a fully nonlinear elliptic equation, appearing in differential geometry, optimal transportation and many other fields in science and engineering. 

While the PDE theory for the Monge-Ampere equation is well developed, relatively few work has been done on its numerical approximation. 

In this talk, I will show a numerical method to the Monge Ampere equation based on its geometric interpretation. 

I will also discuss some of the recent results on the $L^\infty$ and $W^2_p$ error estimate of the Monge-Ampere equation.