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
[21]   Optimal non-dissipative discontinuous Galerkin methods for Maxwell's equations in Drude metamaterials [J].
Li, Jichun ;
Shi, Cengke ;
Shu, Chi-Wang .
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2017, 73 (08) :1760-1780
[22]   Superconvergence of Energy-Conserving Discontinuous Galerkin Methods for Linear Hyperbolic Equations [J].
Liu, Yong ;
Shu, Chi-Wang ;
Zhang, Mengping .
COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION, 2019, 1 (01) :101-116
[23]   Numerical algorithm for the space-time fractional Fokker-Planck system with two internal states [J].
Nie, Daxin ;
Sun, Jing ;
Deng, Weihua .
NUMERISCHE MATHEMATIK, 2020, 146 (03) :481-511
[24]   Nodal discontinuous Galerkin methods for fractional diffusion equations on 2D domain with triangular meshes [J].
Qiu, Liangliang ;
Deng, Weihua ;
Hesthaven, Jan S. .
JOURNAL OF COMPUTATIONAL PHYSICS, 2015, 298 :678-694
[25]  
Sauter SA, 2011, SPR SER COMPUT MATH, V39, P1, DOI 10.1007/978-3-540-68093-2_1
[26]  
Vazquez J.L., 2012, NONLINEAR PARTIAL DI, V7, P271
[27]   Local discontinuous Galerkin methods with explicit-implicit-null time discretizations for solving nonlinear diffusion problems [J].
Wang, Haijin ;
Zhang, Qiang ;
Wang, Shiping ;
Shu, Chi-Wang .
SCIENCE CHINA-MATHEMATICS, 2020, 63 (01) :183-204
[28]   DISCONTINUOUS GALERKIN METHOD FOR FRACTIONAL CONVECTION-DIFFUSION EQUATIONS [J].
Xu, Qinwu ;
Hesthaven, Jan S. .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2014, 52 (01) :405-423
[29]   Space-dependent source determination in a time-fractional diffusion equation using a local discontinuous Galerkin method [J].
Yeganeh, S. ;
Mokhtari, R. ;
Hesthaven, J. S. .
BIT NUMERICAL MATHEMATICS, 2017, 57 (03) :685-707
[30]   A RIESZ BASIS GALERKIN METHOD FOR THE TEMPERED FRACTIONAL LAPLACIAN [J].
Zhang, Zhijiang ;
Deng, Weihua ;
Karniadakis, George Em .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2018, 56 (05) :3010-3039
123