Volume 10, Issue 4
A Local Discontinuous Galerkin Method for Time-Fractional Burgers Equations

Wenping Yuan, Yanping Chen & Yunqing Huang

East Asian J. Appl. Math., 10 (2020), pp. 818-837.

Published online: 2020-08

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  • Abstract

A local discontinuous Galerkin finite element method for a class of timefractional Burgers equations is developed. In order to achieve a high order accuracy, the time-fractional Burgers equation is transformed into a first order system. The method is based on a finite difference scheme in time and local discontinuous Galerkin methods in space. The scheme is proved to be unconditionally stable and in linear case it has convergence rate $\mathcal{O}$(τ2−α + $h$$k$+1), where $k$ ≥ 0 denotes the order of the basis functions used. Numerical examples demonstrate the efficiency and accuracy of the scheme.

  • Keywords

Time-fractional Burgers equation, Caputo fractional derivative, local discontinuous Galerkin method, stability, convergence.

  • AMS Subject Headings

65M60, 35K55

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-10-818, author = {Wenping Yuan , and Yanping Chen , and Yunqing Huang , }, title = {A Local Discontinuous Galerkin Method for Time-Fractional Burgers Equations}, journal = {East Asian Journal on Applied Mathematics}, year = {2020}, volume = {10}, number = {4}, pages = {818--837}, abstract = {

A local discontinuous Galerkin finite element method for a class of timefractional Burgers equations is developed. In order to achieve a high order accuracy, the time-fractional Burgers equation is transformed into a first order system. The method is based on a finite difference scheme in time and local discontinuous Galerkin methods in space. The scheme is proved to be unconditionally stable and in linear case it has convergence rate $\mathcal{O}$(τ2−α + $h$$k$+1), where $k$ ≥ 0 denotes the order of the basis functions used. Numerical examples demonstrate the efficiency and accuracy of the scheme.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.300919.240520}, url = {http://global-sci.org/intro/article_detail/eajam/17963.html} }
TY - JOUR T1 - A Local Discontinuous Galerkin Method for Time-Fractional Burgers Equations AU - Wenping Yuan , AU - Yanping Chen , AU - Yunqing Huang , JO - East Asian Journal on Applied Mathematics VL - 4 SP - 818 EP - 837 PY - 2020 DA - 2020/08 SN - 10 DO - http://doi.org/10.4208/eajam.300919.240520 UR - https://global-sci.org/intro/article_detail/eajam/17963.html KW - Time-fractional Burgers equation, Caputo fractional derivative, local discontinuous Galerkin method, stability, convergence. AB -

A local discontinuous Galerkin finite element method for a class of timefractional Burgers equations is developed. In order to achieve a high order accuracy, the time-fractional Burgers equation is transformed into a first order system. The method is based on a finite difference scheme in time and local discontinuous Galerkin methods in space. The scheme is proved to be unconditionally stable and in linear case it has convergence rate $\mathcal{O}$(τ2−α + $h$$k$+1), where $k$ ≥ 0 denotes the order of the basis functions used. Numerical examples demonstrate the efficiency and accuracy of the scheme.

Wenping Yuan, Yanping Chen & Yunqing Huang. (2020). A Local Discontinuous Galerkin Method for Time-Fractional Burgers Equations. East Asian Journal on Applied Mathematics. 10 (4). 818-837. doi:10.4208/eajam.300919.240520
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