English

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}
}