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Exponential convergence of hp-FEM for the integral fractional Laplacian in 1D

by M. Faustmann and C. Marcati and J.M. Melenk and Ch. Schwab

(Report number 2022-11)

Abstract
We prove weighted analytic regularity for the solution of the integral fractional Poisson problem on bounded intervals with analytic right-hand side. Based on this regularity result, we prove exponential convergence of the \(hp\)-FEM on geometric boundary-refined meshes.

Keywords:

@Techreport{FMMS22_999,
  author = {M. Faustmann and C. Marcati and J.M. Melenk and Ch. Schwab},
  title = {Exponential convergence of hp-FEM for the integral fractional Laplacian in 1D},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2022-11},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2022/2022-11.pdf },
  year = {2022}
}

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