A Posteriori Error Estimates of the Galerkin Spectral Methods for Space-Time Fractional Diffusion Equations

被引：10

作者：

Wang, Huasheng ^{[1
]}

Chen, Yanping ^{[1
]}

Huang, Yunqing ^{[2
]}

Mao, Wenting ^{[1
]}

机构：

[1] South China Normal Univ, Sch Math Sci, Guangzhou 520631, Guangdong, Peoples R China

[2] Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Hunan, Peoples R China

来源：

ADVANCES IN APPLIED MATHEMATICS AND MECHANICS | 2020年 / 12卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Galerkin spectral methods; space-time fractional diffusion equations; a posteriori error estimates; COLLOCATION METHOD; SCHEME;

D O I：

10.4208/aamm.OA-2019-0137

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, an initial boundary value problem of the space-time fractional diffusion equation is studied. Both temporal and spatial directions for this equation are discreted by the Galerkin spectral methods. And then based on the discretization scheme, reliable a posteriori error estimates for the spectral approximation are derived. Some numerical examples are presented to verify the validity and applicability of the derived a posteriori error estimator.

引用

页码：87 / 100

页数：14

共 50 条

[1] A posteriori error estimates of spectral Galerkin methods for multi-term time fractional diffusion equations
Tang, Bo
Chen, Yanping
Lin, Xiuxiu
APPLIED MATHEMATICS LETTERS, 2021, 120
[2] A priori and a posteriori error estimates of a space-time Petrov-Galerkin spectral method for time-fractional diffusion equation
Tang, Bo
Mao, Wenting
Zeng, Zhankuan
MATHEMATICS AND COMPUTERS IN SIMULATION, 2024, 219 : 559 - 572
[3] Error Estimates of Spectral Galerkin Methods for a Linear Fractional Reaction–Diffusion Equation
Zhongqiang Zhang
Journal of Scientific Computing, 2019, 78 : 1087 - 1110
[4] Error estimates of general linear and spectral Galerkin methods for the fractional diffusion equation with spectral fractional Laplacian
Zhang, Yanming
Li, Yu
Yu, Yuexin
Wang, Wansheng
COMPUTATIONAL & APPLIED MATHEMATICS, 2025, 44 (02):
[5] ON A POSTERIORI ERROR ESTIMATES FOR SPACE TIME DISCONTINUOUS GALERKIN METHOD
Dolejsi, Vit
Roskovec, Filip
Vlasak, Miloslav
PROCEEDINGS OF THE CONFERENCE ALGORITMY 2016, 2016, : 125 - 134
[6] A POSTERIORI ERROR ESTIMATES FOR HIGHER ORDER SPACE-TIME GALERKIN DISCRETIZATIONS OF NONLINEAR PARABOLIC PROBLEMS
Dolejsi, Vit
Roskovec, Filip
Vlasak, Miloslav
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2021, 59 (03) : 1486 - 1509
[7] Error Estimates of Spectral Galerkin Methods for a Linear Fractional Reaction-Diffusion Equation
Zhang, Zhongqiang
JOURNAL OF SCIENTIFIC COMPUTING, 2019, 78 (02) : 1087 - 1110
[8] A Space-Time Petrov-Galerkin Spectral Method for Time Fractional Diffusion Equation
Sheng, Changtao
Shen, Jie
NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, 2018, 11 (04) : 854 - 876
[9] POINTWISE A POSTERIORI ERROR ESTIMATES FOR DISCONTINUOUS GALERKIN METHODS FOR SINGULARLY PERTURBED REACTION-DIFFUSION EQUATIONS
Kopteva, Natalia
Rankin, Richard
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2023, 61 (04) : 1938 - 1961
[10] A posteriori discontinuous Galerkin error estimates for transient convection-diffusion equations
Ern, A
Proft, J
APPLIED MATHEMATICS LETTERS, 2005, 18 (07) : 833 - 841

← 1 2 3 4 5 →