Faustmann, M., Marcati, C., Melenk, J. M., & Schwab, C. (2023). Exponential Convergence of hp-FEM for the Integral Fractional Laplacian in Polygons. SIAM Journal on Numerical Analysis, 61(6), 2601–2622. https://doi.org/10.1137/22M152493X
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.
