The second boundary value problem for a discrete Monge-Ampere equation
Numerical Analysis
2024-07-11 v5 Numerical Analysis
Abstract
In this work we propose a discretization of the second boundary condition for the Monge-Ampere equation arising in geometric optics and optimal transport. The discretization we propose is the natural generalization of the popular Oliker-Prussner method proposed in 1988. For the discretization of the differential operator, we use a discrete analogue of the subdifferential. Existence, unicity and stability of the solutions to the discrete problem are established. Convergence results to the continuous problem are given.
Keywords
Cite
@article{arxiv.1910.14376,
title = {The second boundary value problem for a discrete Monge-Ampere equation},
author = {Gerard Awanou},
journal= {arXiv preprint arXiv:1910.14376},
year = {2024}
}