We develop a monotone, two-scale discretization for a class of integrodifferential operators of order $2s$, $s \in (0,1)$. We apply it to develop numerical schemes, and derive pointwise convergence rates, for linear and obstacle problems governed by such operators. As applications of the monotonicity, we provide error estimates for free boundaries and a convergent numerical scheme for a concave fully nonlinear, nonlocal, problem.

翻译：我们针对一类阶数为 $2s$（$s \in (0,1)$）的积分-微分算子，提出了一种单调的双尺度离散化方法。我们将该方法应用于数值格式的构建，并针对由这类算子控制的线性问题及障碍问题，推导了逐点收敛速率。作为单调性的应用，我们给出了自由边界问题的误差估计，并针对一个凹性完全非线性非局部问题提出了收敛的数值格式。