Geodesic
The local discontinuous Galerkin method with generalized alternating flux for solving Burger's equation
Zhang, Rongpei 1 ; Wang, Di 1 ; Yu, Xijun 2 ; Chen, Bo 3 ; Wang, Zhen 4
1 School of Mathematics and Systematic Sciences, Shenyang Normal University, Shenyang 110034, P. R. China
2 Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, P. R. China
3 College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, P. R. China
4 College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, P. R. China
Journal of nonlinear sciences and its applications, Tome 12 (2019) no. 5, p. 300-313.

Voir la notice de l'article provenant de la source International Scientific Research Publications

In this paper, we propose the local discontinuous Galerkin method based on the generalized alternating numerical flux for solving the one-dimensional nonlinear Burger's equation with Dirichlet boundary conditions. Based on the Hopf-Cole transformation, the original equation is transformed into a linear heat conduction equation with homogeneous Neumann boundary conditions. We will show that this method preserves stability. By virtue of the generalized Gauss-Radau projection, we can obtain the sub-optimal rate of convergence in $L^2$-norm of $\mathcal{O}(h^{k+\frac{1}{2}})$ with polynomial of degree $k$ and grid size $h$. Numerical experiments are given to verify the theoretical results.
DOI : 10.22436/jnsa.012.05.04
Classification : 65M60
Keywords: Burger's equation, local discontinuous Galerkin method, Hopf-Cole transformation, generalized alternating numerical flux, generalized Gauss-Radau projection

Zhang, Rongpei  1 ; Wang, Di  1 ; Yu, Xijun  2 ; Chen, Bo  3 ; Wang, Zhen  4

1 School of Mathematics and Systematic Sciences, Shenyang Normal University, Shenyang 110034, P. R. China
2 Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, P. R. China
3 College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, P. R. China
4 College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, P. R. China 
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Zhang, Rongpei ; Wang, Di ; Yu, Xijun ; Chen, Bo ; Wang, Zhen . The local discontinuous Galerkin method with generalized alternating flux for solving Burger's equation. Journal of nonlinear sciences and its applications, Tome 12 (2019) no. 5, p. 300-313. doi : 10.22436/jnsa.012.05.04. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.012.05.04/

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