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 .
Exponential Convergence of hp-FEM for the Integral Fractional Laplacian in Polygons
Carlo Marcati;
2023-01-01
Abstract
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 .File in questo prodotto:
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