Local convergence of the FEM for the integral fractional Laplacian

Abstract

We provide for first order discretizations of the integral fractional Laplacian sharp local error estimates on proper subdomains in both the local $H^1$-norm and the localized energy norm. Our estimates have the form of a local best approximation error plus a global error measured in a weaker norm.

References in corpus (14)

• An extension problem related to the fractional Laplacian
• Ten equivalent definitions of the fractional Laplace operator
• Fractional Laplacians on domains, a development of Hörmander's theory of mu-transmission pseudodifferential operators
• A fractional Laplace equation: regularity of solutions and Finite Element approximations
• Numerical Methods for Fractional Diffusion
• A short FE implementation for a 2d homogeneous Dirichlet problem of a Fractional Laplacian
• Aspects of an adaptive finite element method for the fractional Laplacian: a priori and a posteriori error estimates, efficient implementation and multigrid solver
• Local high-order regularization and applications to hp-methods
• Tensor FEM for spectral fractional diffusion
• Hybrid Finite Element - Spectral Method for the Fractional Laplacian: Approximation Theory and Efficient Solver
• Instance optimality of the adaptive maximum strategy
• $\mathcal{H}$-matrix approximability of inverses of discretizations of the fractional Laplacian
• Finite element approximations of the nonhomogeneous fractional Dirichlet problem
• Local convergence of the boundary element method on polyhedral domains

Cited by in corpus (5)

• Weighted analytic regularity for the integral fractional Laplacian in polygons
• Exponential Convergence of hp FEM for the Integral Fractional Laplacian in Polygons
• A grid-overlay finite difference method for the fractional Laplacian on arbitrary bounded domains
• Meshfree finite difference solution of homogeneous Dirichlet problems of the fractional Laplacian
• Approximating and preconditioning the stiffness matrix in the GoFD approximation of the fractional Laplacian