Optimisation approach for the Monge-Ampere equation
Analysis of PDEs
2017-01-20 v1
Abstract
This paper studies the numerical approximation of solution of the Dirichlet problem for the fully nonlinear Monge-Ampere equation. In this approach, we take the advantage of reformulation the Monge-Ampere problem as an optimization problem, to which we associate a well defined functional whose minimum provides us with the solution to the Monge-Ampere problem after resolving a Poisson problem by the finite element Galerkin method. We present some numerical examples, for which a good approximation is obtained in 68 iterations.
Cite
@article{arxiv.1701.05388,
title = {Optimisation approach for the Monge-Ampere equation},
author = {Fethi Ben Belgacem},
journal= {arXiv preprint arXiv:1701.05388},
year = {2017}
}
Comments
This paper contains 11 pages