Exponential Convergence of hp FEM for the Integral Fractional Laplacian in Polygons

We prove exponential convergence in the energy norm of $hp$ finite element discretizations for the integral fractional diffusion operator of order $2s\in (0,2)$ subject to homogeneous Dirichlet boundary conditions in bounded polygonal domains $\mathrm{\Omega }\subset {\mathbb{R}}^2$. Key ingredient in the analysis are the weighted analytic regularity from our previous work and meshes that feature anisotropic geometric refinement towards $\mathrm{\partial }\mathrm{\Omega }$.