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 Laplacian of order 2s ∈ (0, 2) subject to homogeneous Dirichlet boundary conditions in bounded polygonal domains Ω ⊂ R2. Key ingredients in the analysis are the weighted analytic regularity from [M. Faustmann, C. Marcati, J. M. Melenk, and C. Schwab, SIAM J. Math. Anal., 54 (2022), pp. 6323-6357] and meshes that feature anisotropic geometric refinement towards ∂Ω .