The local discontinuous Galerkin finite element method for Burger's equation

The local discontinuous Galerkin finite element method for Burger's equation
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DOI：
10.1016/j.mcm.2011.07.016
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发表时间：
2011-12
期刊：
Math. Comput. Model.
影响因子：
--
通讯作者：
Long Shao;Xinlong Feng;Yinnian He
Long Shao;Xinlong Feng;Yinnian He
中科院分区：
其他
文献类型：
--
作者：
Long Shao;Xinlong Feng;Yinnian He

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In this paper, we study the local discontinuous Galerkin (LDG) finite element method for solving a nonlinear Burger’s equation with Dirichlet boundary conditions. Based on the Hopf–Cole transformation, we transform the original problem into a linear heat equation with Neumann boundary conditions. The heat equation is then solved by the LDG finite element method with special chosen numerical flux. Theoretical analysis shows that this method is stable and the (k+1)th order of convergence rate when the polynomials Pkare used. Finally, we present some examples of Pkpolynomials with 1≤k≤4 to demonstrate the high-order accuracy of this method. The numerical results are also shown to be more accurate than some available results given in the literature.