Exponential Convergence of hp FEM for the Integral Fractional Laplacian in Polygons

Abstract

We prove exponential convergence in the energy norm of $hp$ finite element discretizations for the integral fractional diffusion operator of order $2s\in (0,2)$ subject to homogeneous Dirichlet boundary conditions in bounded polygonal domains $\Omega \subset {\mathbb{R}}^2$. Key ingredient in the analysis are the weighted analytic regularity from our previous work and meshes that feature anisotropic geometric refinement towards $\partial \Omega$.

References in corpus (5)

• Numerical methods for nonlocal and fractional models
• Local convergence of the FEM for the integral fractional Laplacian
• Weighted analytic regularity for the integral fractional Laplacian in polygons
• Exponential Convergence of $hp$ FEM for Spectral Fractional Diffusion in Polygons
• Exponential convergence of hp-FEM for the integral fractional Laplacian in 1D

Cited by in corpus (2)

• Fractional Dissipative PDEs
• Caloric functions and boundary regularity for the fractional Laplacian in Lipschitz open sets