Monotone two-scale methods for a class of integrodifferential operators and applications

Abstract

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.