Pseudo transient continuation and time marching methods for Monge-Ampere type equations
Numerical Analysis
2014-07-01 v4
Abstract
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.
Cite
@article{arxiv.1301.5891,
title = {Pseudo transient continuation and time marching methods for Monge-Ampere type equations},
author = {Gerard Awanou},
journal= {arXiv preprint arXiv:1301.5891},
year = {2014}
}