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

09/23/2022

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by   Markus Faustmann, et al.

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