Convergent approaches for the Dirichlet Monge amp\`ere problem
Numerical Analysis
2023-01-23 v1 Numerical Analysis
Abstract
In this article, we introduce and study three numerical methods for the Dirichlet Monge Amp\`ere equation in two dimensions. The approaches consist in considering new equivalent problems. The latter are discretized by a wide stencil finite difference discretization and monotone schemes are obtained. Hence, we apply the Barles-Souganidis theory to prove the convergence of the schemes and the Damped Newtons method is used to compute the solutions of the schemes. Finally, some numerical results are illustrated.
Cite
@article{arxiv.2301.08636,
title = {Convergent approaches for the Dirichlet Monge amp\`ere problem},
author = {Hajri Imen and Fethi Ben Belgacem},
journal= {arXiv preprint arXiv:2301.08636},
year = {2023}
}
Comments
14pages, 7figures