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

Markus Faustmann, Carlo Marcati, Jens Markus Melenk, Christoph Schwab

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.