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.

翻译：本文提出了几何光学与最优输运中Monge-Ampère方程第二边界条件的一种离散化方法。所提出的离散化是1988年经典的Oliker-Prussner方法的自然推广。对于微分算子的离散化，我们使用了次微分的离散模拟。建立了离散问题解的存在性、唯一性和稳定性，并给出了向连续问题的收敛性结果。