Quasi-optimal convergence rate for an adaptive method for the integral fractional Laplacian

For the discretization of integral fractional Laplacian $(-\Delta )^s$, $0 < s 1$, based on piecewise linear functions, we present and analyze a reliable weighted residual posteriori error estimator. In order to compensate for lack $L^2$-regularity in regime $3/4 this estimator includes as an additional weight power distance from mesh skeleton. We prove optimal convergence rates $h$-adaptive algorithm driven by Key analysis adaptive are local inverse estimates Laplacian.