Exponential Convergence of \(hp\)-FEM for the Integral Fractional Laplacian in Polygons
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Date
2023-12-31Type
- Journal Article
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Abstract
We prove exponential convergence in the energy norm of \(hp\)-finite element discretizations for the integral fractional Laplacian of order \(2s\in (0,2)\) subject to homogeneous Dirichlet boundary conditions in bounded polygonal domains \(\Omega \subset{\mathbb R}^2\). 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 \(\partial \Omega\). Show more
Publication status
publishedExternal links
Journal / series
SIAM Journal on Numerical AnalysisVolume
Pages / Article No.
Publisher
SIAMSubject
Fractional Laplacian; Corner domains; hp-FEM; Exponential convergenceOrganisational unit
03435 - Schwab, Christoph / Schwab, Christoph
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Is new version of: http://hdl.handle.net/20.500.11850/574430
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ETH Bibliography
yes
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