A Local Discontinuous Galerkin Method for the Camassa-Holm Equation
A Local Discontinuous Galerkin Method for the Camassa-Holm Equation
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DOI：
10.1137/070679764
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发表时间：
2008-04
期刊：
影响因子：
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通讯作者：
Yan Xu;Chi-Wang Shu
中科院分区：
文献类型：
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作者：
Yan Xu;Chi-Wang Shu
在本文中，我们开发，分析和测试的局部间断Galerkin（LDG）方法求解Camassa-Holm方程，其中包含非线性高阶导数。LDG方法具有任意h和p自适应的灵活性。我们证明了一般解的L^2 $稳定性，给出了光滑解的详细误差估计，并对非线性Camassa-Holm方程的不同类型的解进行了数值模拟，以说明LDG方法的精度和能力.
In this paper, we develop, analyze, and test a local discontinuous Galerkin (LDG) method for solving the Camassa–Holm equation which contains nonlinear high-order derivatives. The LDG method has the flexibility for arbitrary h and p adaptivity. We prove the $L^2$ stability for general solutions and give a detailed error estimate for smooth solutions, and provide numerical simulation results for different types of solutions of the nonlinear Camassa–Holm equation to illustrate the accuracy and capability of the LDG method.