Direct discontinuous Galerkin method for the generalized Burgers–Fisher equation

doi:10.1088/1674-1056/21/9/090206

中国物理B ›› 2012, Vol. 21 ›› Issue (9): 90206-090206.doi: 10.1088/1674-1056/21/9/090206

Direct discontinuous Galerkin method for the generalized Burgers–Fisher equation

张荣培^a, 张立伟^{b c}

a School of Sciences, Liaoning Shihua University, Fushun 113001, China;
b Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China;
c The Chinese University of Hong Kong, Hong Kong, China

收稿日期:2012-01-05 修回日期:2012-02-14 出版日期:2012-08-01 发布日期:2012-08-01
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 61105130 and 61175124).

Direct discontinuous Galerkin method for the generalized Burgers–Fisher equation

Zhang Rong-Pei (张荣培)^a, Zhang Li-Wei (张立伟)^{b c}

a School of Sciences, Liaoning Shihua University, Fushun 113001, China;
b Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China;
c The Chinese University of Hong Kong, Hong Kong, China

Received:2012-01-05 Revised:2012-02-14 Online:2012-08-01 Published:2012-08-01
Contact: Zhang Rong-Pei E-mail:rongpeizhang@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 61105130 and 61175124).

摘要/Abstract

摘要： In this study, we use the direct discontinuous Galerkin method to solve the generalized Burgers-Fisher equation. The method is based on the direct weak formulation of the Burgers-Fisher equation. The two adjacent cells are jointed by a numerical flux that includes the convection numerical flux and the diffusion numerical flux. We solve the ordinary differential equations arising in the direct Galerkin method by using the strong stability preserving Runge-Kutta method. Numerical results are compared with the exact solution and the other results to show the accuracy and reliability of the method.

关键词: direct discontinuous Galerkin method, Burgers-Fisher equation, strong stability preserving Runge-Kutta method

Abstract: In this study, we use the direct discontinuous Galerkin method to solve the generalized Burgers-Fisher equation. The method is based on the direct weak formulation of the Burgers-Fisher equation. The two adjacent cells are jointed by a numerical flux that includes the convection numerical flux and the diffusion numerical flux. We solve the ordinary differential equations arising in the direct Galerkin method by using the strong stability preserving Runge-Kutta method. Numerical results are compared with the exact solution and the other results to show the accuracy and reliability of the method.

Key words: direct discontinuous Galerkin method, Burgers-Fisher equation, strong stability preserving Runge-Kutta method

中图分类号: (Finite-element and Galerkin methods)

02.70.Dh

52.35.-g (Waves, oscillations, and instabilities in plasmas and intense beams)

张荣培, 张立伟. Direct discontinuous Galerkin method for the generalized Burgers–Fisher equation[J]. 中国物理B, 2012, 21(9): 90206-090206.

Zhang Rong-Pei (张荣培), Zhang Li-Wei (张立伟). Direct discontinuous Galerkin method for the generalized Burgers–Fisher equation[J]. Chin. Phys. B, 2012, 21(9): 90206-090206.

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Direct discontinuous Galerkin method for the generalized Burgers–Fisher equation

Direct discontinuous Galerkin method for the generalized Burgers–Fisher equation

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