Discrete Aleksandrov solutions of the Monge-Ampere equation

2014/08/07 by Awanou, Gerard
#35J60 #39A12 #65M06 #65N12 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1408.1729

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.

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