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Chin. Phys. B, 2012, Vol. 21(9): 090206    DOI: 10.1088/1674-1056/21/9/090206
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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
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.
Keywords:  direct discontinuous Galerkin method      Burgers-Fisher equation      strong stability preserving Runge-Kutta method  
Received:  05 January 2012      Revised:  14 February 2012      Accepted manuscript online: 
PACS:  02.70.Dh (Finite-element and Galerkin methods)  
  52.35.-g (Waves, oscillations, and instabilities in plasmas and intense beams)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 61105130 and 61175124).
Corresponding Authors:  Zhang Rong-Pei     E-mail:  rongpeizhang@163.com

Cite this article: 

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

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