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Volume 12, Issue 1
A Posteriori Error Estimates of the Galerkin Spectral Methods for Space-Time Fractional Diffusion Equations

Huasheng Wang, Yanping Chen, Yunqing Huang & Wenting Mao

DOI: 10.4208/aamm.OA-2019-0137

Adv. Appl. Math. Mech., 12 (2020), pp. 87-100.

Published online: 2019-12

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  • Abstract

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.

  • Keywords

Galerkin spectral methods, space-time fractional diffusion equations, a posteriori error estimates.

  • AMS Subject Headings

65M12, 65M70

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

huashengwang123@163.com (Huasheng Wang)

yanpingchen@scnu.edu.cn (Yanping Chen)

huangyq@xtu.edu.cn (Yunqing Huang)

maowenting126@163.com (Wenting Mao)

  • BibTex
  • RIS
  • TXT
@Article{AAMM-12-87, author = {Wang , HuashengChen , YanpingHuang , Yunqing and Mao , Wenting}, title = {A Posteriori Error Estimates of the Galerkin Spectral Methods for Space-Time Fractional Diffusion Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2019}, volume = {12}, number = {1}, pages = {87--100}, abstract = {

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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2019-0137}, url = {http://global-sci.org/intro/article_detail/aamm/13420.html} }
TY - JOUR T1 - A Posteriori Error Estimates of the Galerkin Spectral Methods for Space-Time Fractional Diffusion Equations AU - Wang , Huasheng AU - Chen , Yanping AU - Huang , Yunqing AU - Mao , Wenting JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 87 EP - 100 PY - 2019 DA - 2019/12 SN - 12 DO - http://doi.org/10.4208/aamm.OA-2019-0137 UR - https://global-sci.org/intro/article_detail/aamm/13420.html KW - Galerkin spectral methods, space-time fractional diffusion equations, a posteriori error estimates. AB -

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.

Wang , HuashengChen , YanpingHuang , Yunqing and Mao , Wenting. (2019). A Posteriori Error Estimates of the Galerkin Spectral Methods for Space-Time Fractional Diffusion Equations. Advances in Applied Mathematics and Mechanics. 12 (1). 87-100. doi:10.4208/aamm.OA-2019-0137
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