Pseudo transient continuation and time marching methods for Monge-Ampere type equations
For researchers in numerical PDEs, this provides provably convergent methods for a challenging nonlinear equation, though the approach is incremental.
The paper presents two numerical methods for solving the fully nonlinear elliptic Monge-Ampere equation, proving convergence to a strictly convex solution for a discrete variational formulation with C1 conforming approximations. The methods are validated for smooth solutions and supported by numerical evidence for non-smooth cases.
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 $C^1$ 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.