Discrete Aleksandrov solutions of the Monge-Ampere equation
Numerical Analysis
2019-11-01 v4 Numerical Analysis
Abstract
We prove the convergence of a wide stencil finite difference scheme to the Aleksandrov solution of the elliptic Monge-Ampere equation when the right hand side is a sum of Dirac masses. The discrete scheme we analyze for the Dirichlet problem, when coupled with a discretization of the second boundary condition, can be used to get a good initial guess for geometric methods solving optimal transport between two measures.
Keywords
Cite
@article{arxiv.1408.1729,
title = {Discrete Aleksandrov solutions of the Monge-Ampere equation},
author = {Gerard Awanou},
journal= {arXiv preprint arXiv:1408.1729},
year = {2019}
}