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Pseudo transient continuation and time marching methods for Monge-Ampere type equations
We present two numerical methods for the fully nonlinear elliptic
Monge-Ampere 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 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