Constructive approximation on graded meshes for the integral fractional Laplacian
Numerical Analysis
2022-12-29 v3 Numerical Analysis
Analysis of PDEs
Abstract
We consider the homogeneous Dirichlet problem for the integral fractional Laplacian . We prove optimal Sobolev regularity estimates in Lipschitz domains provided the solution is up to the boundary. We present the construction of graded bisection meshes by a greedy algorithm and derive quasi-optimal convergence rates for approximations to the solution of such a problem by continuous piecewise linear functions. The nonlinear Sobolev scale dictates the relation between regularity and approximability.
Cite
@article{arxiv.2109.00451,
title = {Constructive approximation on graded meshes for the integral fractional Laplacian},
author = {Juan Pablo Borthagaray and Ricardo H. Nochetto},
journal= {arXiv preprint arXiv:2109.00451},
year = {2022}
}