Constructive Approximation on Graded Meshes for the Integral Fractional Laplacian

被引：4
|
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
收藏
页码：463 / 487
页数：25
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