Pseudo transient continuation and time marching methods for Monge-Ampère type equations

We present two numerical methods for the fully nonlinear elliptic Monge-Ampère equation. The first is a pseudo transient continuation method and the second is a pure pseudo time marching method. The methods are proven to converge to a strictly convex solution of a natural discrete variational formulation with C1 conforming approximations. The assumption of existence of a strictly convex solution to the discrete problem is proven for smooth solutions of the continuous problem and supported by numerical evidence for non smooth solutions.