<div class="csl-bib-body">
<div class="csl-entry">Faustmann, M., Marcati, C., Melenk, J. M., & Schwab, C. (2023). Exponential Convergence of hp-FEM for the Integral Fractional Laplacian in Polygons. <i>SIAM Journal on Numerical Analysis</i>, <i>61</i>(6), 2601–2622. https://doi.org/10.1137/22M152493X</div>
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dc.identifier.issn
0036-1429
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/190059
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dc.description.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.
en
dc.language.iso
en
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dc.publisher
SIAM PUBLICATIONS
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dc.relation.ispartof
SIAM Journal on Numerical Analysis
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dc.subject
fractional Laplacian
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dc.subject
corner domains
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dc.subject
hp-FEM
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dc.subject
exponential convergence
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dc.title
Exponential Convergence of hp-FEM for the Integral Fractional Laplacian in Polygons
