Direct discontinuous Galerkin method for the generalized Burgers–Fisher equation

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

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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