Constructive Approximation on Graded Meshes for the Integral Fractional Laplacian

被引：6

作者：

Borthagaray, Juan Pablo ^{[1
,2
]}

Nochetto, Ricardo H. ^{[3
]}

机构：

[1] Univ Republ, Dept Matemat & Estadist Litoral, Salto, Uruguay

[2] Univ Republica, Ctr Matemat, Montevideo, Uruguay

[3] Univ Maryland, Inst Phys Sci & Technol, Dept Math, College Pk, MD 20742 USA

来源：

CONSTRUCTIVE APPROXIMATION | 2023年 / 57卷 / 02期

关键词：

integral fractional Laplacian; graded Meshes; greedy algorithm; ARONSZAJN-SLOBODECKIJ NORM; BOUNDARY-ELEMENT METHODS; ELLIPTIC PROBLEMS; NUMERICAL-METHODS; REGULARITY; INTERPOLATION; LOCALIZATION; DOMAINS;

D O I：

10.1007/s00365-023-09617-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the homogeneous Dirichlet problem for the integral fractional Laplacian (-delta)(s). We prove optimal Sobolev regularity estimates in Lipschitz domains pro-vided the solution is C-s 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.

引用

页码：463 / 487

页数：25

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