Local discontinuous Galerkin method for the fractional diffusion equation with integral fractional Laplacian

被引：3
作者：
Nie, Daxin [1 ]
Deng, Weihua [1 ]
机构：
[1] Lanzhou Univ, Sch Math & Stat, Gansu Key Lab Appl Math & Complex Syst, Lanzhou 730000, Peoples R China
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2021年 / 104卷
基金：
中国国家自然科学基金;
关键词：
Local discontinuous Galerkin method; Integral fractional Laplacian; Stability analysis; Error estimates; NUMERICAL-METHODS; SUPERCONVERGENCE; REGULARITY;
D O I：
10.1016/j.camwa.2021.11.007
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we provide a framework of designing the local discontinuous Galerkin scheme for integral fractional Laplacian (-Delta)(s) with s is an element of (0, 1) in two dimensions. We theoretically prove and numerically verify the numerical stability and convergence of the scheme with the convergence rate no worse than O(h(k)(+1/2)) with k >= 1.
引用
收藏
页码：44 / 49
页数：6
相关论文
共 30 条
[1]   FINITE ELEMENT APPROXIMATIONS FOR FRACTIONAL EVOLUTION PROBLEMS [J].
Acosta, Gabriel ;
Bersetche, Francisco M. ;
Pablo Borthagaray, Juan .
FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2019, 22 (03) :767-794
[2]   Finite element approximations of the nonhomogeneous fractional Dirichlet problem [J].
Acosta, Gabriel ;
Pablo Borthagaray, Juan ;
Heuer, Norbert .
IMA JOURNAL OF NUMERICAL ANALYSIS, 2019, 39 (03) :1471-1501
[3]   REGULARITY THEORY AND HIGH ORDER NUMERICAL METHODS FOR THE (1D)-FRACTIONAL LAPLACIAN [J].
Acosta, Gabriel ;
Pablo Borthagaray, Juan ;
Bruno, Oscar ;
Maas, Martin .
MATHEMATICS OF COMPUTATION, 2018, 87 (312) :1821-1857
[4]   A short FE implementation for a 2d homogeneous Dirichlet problem of a fractional Laplacian [J].
Acosta, Gabriel ;
Bersetche, Francisco M. ;
Pablo Borthagaray, Juan .
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2017, 74 (04) :784-816
[5]   A FRACTIONAL LAPLACE EQUATION: REGULARITY OF SOLUTIONS AND FINITE ELEMENT APPROXIMATIONS [J].
Acosta, Gabriel ;
Pablo Borthagaray, Juan .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2017, 55 (02) :472-495
[6]   Numerical approximation of the integral fractional Laplacian [J].
Bonito, Andrea ;
Lei, Wenyu ;
Pasciak, Joseph E. .
NUMERISCHE MATHEMATIK, 2019, 142 (02) :235-278
[7]   On the Convergence of the Local Discontinuous Galerkin Method Applied to a Stationary One Dimensional Fractional Diffusion Problem [J].
Castillo, P. ;
Gomez, S. .
JOURNAL OF SCIENTIFIC COMPUTING, 2020, 85 (02)
[8]  
Castillo P, 2002, MATH COMPUT, V71, P455, DOI 10.1090/S0025-5718-01-01317-5
[9]   Optimal stabilization and time step constraints for the forward Euler-Local Discontinuous Galerkin method applied to fractional diffusion equations [J].
Castillo, Paul ;
Gomez, Sergio .
JOURNAL OF COMPUTATIONAL PHYSICS, 2019, 394 :503-521
[10]   The local discontinuous Galerkin method for time-dependent convection-diffusion systems [J].
Cockburn, B ;
Shu, CW .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1998, 35 (06) :2440-2463
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