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Volume 42, Issue 1
A Direct Discontinuous Galerkin Method for Time Fractional Diffusion Equations with Fractional Dynamic Boundary Conditions

Jingjun Zhao, Wenjiao Zhao & Yang Xu

DOI: 10.4208/jcm.2203-m2021-0233

J. Comp. Math., 42 (2024), pp. 156-177.

Published online: 2023-12

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  • Abstract

This paper deals with the numerical approximation for the time fractional diffusion problem with fractional dynamic boundary conditions. The well-posedness for the weak solutions is studied. A direct discontinuous Galerkin approach is used in spatial direction under the uniform meshes, together with a second-order Alikhanov scheme is utilized in temporal direction on the graded mesh, and then the fully discrete scheme is constructed. Furthermore, the stability and the error estimate for the full scheme are analyzed in detail. Numerical experiments are also given to illustrate the effectiveness of the proposed method.

  • Keywords

Time fractional diffusion equation, Numerical stability, Convergence.

  • AMS Subject Headings

65M12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-42-156, author = {Zhao , JingjunZhao , Wenjiao and Xu , Yang}, title = {A Direct Discontinuous Galerkin Method for Time Fractional Diffusion Equations with Fractional Dynamic Boundary Conditions}, journal = {Journal of Computational Mathematics}, year = {2023}, volume = {42}, number = {1}, pages = {156--177}, abstract = {

This paper deals with the numerical approximation for the time fractional diffusion problem with fractional dynamic boundary conditions. The well-posedness for the weak solutions is studied. A direct discontinuous Galerkin approach is used in spatial direction under the uniform meshes, together with a second-order Alikhanov scheme is utilized in temporal direction on the graded mesh, and then the fully discrete scheme is constructed. Furthermore, the stability and the error estimate for the full scheme are analyzed in detail. Numerical experiments are also given to illustrate the effectiveness of the proposed method.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2203-m2021-0233}, url = {http://global-sci.org/intro/article_detail/jcm/22156.html} }
TY - JOUR T1 - A Direct Discontinuous Galerkin Method for Time Fractional Diffusion Equations with Fractional Dynamic Boundary Conditions AU - Zhao , Jingjun AU - Zhao , Wenjiao AU - Xu , Yang JO - Journal of Computational Mathematics VL - 1 SP - 156 EP - 177 PY - 2023 DA - 2023/12 SN - 42 DO - http://doi.org/10.4208/jcm.2203-m2021-0233 UR - https://global-sci.org/intro/article_detail/jcm/22156.html KW - Time fractional diffusion equation, Numerical stability, Convergence. AB -

This paper deals with the numerical approximation for the time fractional diffusion problem with fractional dynamic boundary conditions. The well-posedness for the weak solutions is studied. A direct discontinuous Galerkin approach is used in spatial direction under the uniform meshes, together with a second-order Alikhanov scheme is utilized in temporal direction on the graded mesh, and then the fully discrete scheme is constructed. Furthermore, the stability and the error estimate for the full scheme are analyzed in detail. Numerical experiments are also given to illustrate the effectiveness of the proposed method.

Zhao , JingjunZhao , Wenjiao and Xu , Yang. (2023). A Direct Discontinuous Galerkin Method for Time Fractional Diffusion Equations with Fractional Dynamic Boundary Conditions. Journal of Computational Mathematics. 42 (1). 156-177. doi:10.4208/jcm.2203-m2021-0233
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