$\mathcal{H}$-matrix approximability of inverses of discretizations of the fractional Laplacian

Abstract

The integral version of the fractional Laplacian on a bounded domain is discretized by a Galerkin approximation based on piecewise linear functions on a quasi-uniform mesh. We show that the inverse of the associated stiffness matrix can be approximated by blockwise low-rank matrices at an exponential rate in the block rank.

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Cited by in corpus (7)

• 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 Polygons
• Exponential convergence of hp-FEM for the integral fractional Laplacian in 1D
• Tensor Method for Optimal Control Problems Constrained by Fractional 3D Elliptic Operator with Variable Coefficients
• Caccioppoli-type estimates and $\mathcal{H}$-Matrix approximations to inverses for FEM-BEM couplings