Second-Order Finite Difference/Spectral Element Formulation for Solving the Fractional Advection-Diffusion Equation

被引：15
|
作者：
Abbaszadeh, Mostafa [1 ]
Amjadian, Hanieh [1 ]
机构：
[1] Amirkabir Univ Technol, Dept Appl Math, Fac Math & Comp Sci, 424 Hafez Ave, Tehran 15914, Iran
来源：
COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION | 2020年 / 2卷 / 04期
关键词：
Spectral method; Finite difference method; Fractional advection-diffusion equation; Galerkin weak form; Unconditional stability; 65L60; 65L20; 65M70; PARTIAL-DIFFERENTIAL-EQUATION; TIME SPECTRAL METHOD; NUMERICAL ALGORITHM; COLLOCATION METHOD; ERROR ESTIMATE; WAVE EQUATION; SPACE; APPROXIMATIONS; SCHEME; DERIVATIVES;
D O I：
10.1007/s42967-020-00060-y
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The main aim of this paper is to analyze the numerical method based upon the spectral element technique for the numerical solution of the fractional advection-diffusion equation. The time variable has been discretized by a second-order finite difference procedure. The stability and the convergence of the semi-discrete formula have been proven. Then, the spatial variable of the main PDEs is approximated by the spectral element method. The convergence order of the fully discrete scheme is studied. The basis functions of the spectral element method are based upon a class of Legendre polynomials. The numerical experiments confirm the theoretical results.
引用
收藏
页码：653 / 669
页数：17
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