An efficient approach for the numerical solution of the Monge–Ampère equation

In this paper, we present a new method to compute the numerical solution of the elliptic Monge–Ampère equation. This method is based on solving a parabolic Monge–Ampère equation for the steady state solution. We study the problem of global existence, uniqueness, and convergence of the solution of the fully nonlinear parabolic PDE to the unique solution of the elliptic Monge–Ampère equation. Some numerical experiments are presented to show the convergence and the regularity of the numerical solution.