| Direct discontinuous Galerkin method for the generalized Burgers—Fisher equation |
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| 引用本文： | 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. |
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| 作者姓名： | 张荣培 张立伟 |
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| 作者单位： | School of Sciences, Liaoning Shihua University;Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences;The Chinese University of Hong Kong |
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| 基金项目： | Project supported by the National Natural Science Foundation of China （Grant Nos. 61105130 and 61175124）. |
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| 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.
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| 关 键 词： | direct discontinuous Galerkin method Burgers-Fisher equation strong stability preserving Runge-Kutta method |
| 收稿时间： | 2012-01-05 |
Direct discontinuous Galerkin method for the generalized Burgers-Fisher equation |
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| Zhang Rong-Pei,Zhang Li-Wei.Direct discontinuous Galerkin method for the generalized Burgers-Fisher equation[J].Chinese Physics B,2012,21(9):90206-090206. |
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| Authors: | Zhang Rong-Pei Zhang Li-Wei |
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| Institution: | 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 |
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| 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. |
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| Keywords: | direct discontinuous Galerkin method Burgers-Fisher equation strong stability preserving Runge-Kutta method |
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