| Spectral Element Viscosity Methods for Nonlinear Conservation Laws onthe Semi-Infinite Interval |
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| 作者姓名： | Liang Jiang Chuanju Xu |
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| 作者单位： | Liang Jiang (Department of Mathematics，Putian University，Putian 351115，China Chuanju Xu (Department of Mathematics，Xiamen University，Xiamen 361005，China |
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| 基金项目： | 国家自然科学基金
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the Excellent Young Teachers Program by the Ministry of Education of China
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国家重点基础研究发展计划(973计划) |
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| 摘 要： | In this paper we propose a spectral element: vanishing viscosity (SEW) method for the conservation laws on the semi-infinite interval. By using a suitable mapping, the problem is first transformed into a modified conservation law in a bounded interval, then the well-known spectral vanishing viscosity technique is generalized to the multi-domain case in order to approximate this trarsformed equation more efficiently. The construction details and convergence analysis are presented. Under a usual assumption of boundedness of the approximation solutions, it is proven that the solution of the SEW approximation converges to the uniciue entropy solution of the conservation laws. A number of numerical tests is carried out to confirm the theoretical results.
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| 关 键 词： | 半无穷区间 非线性守恒定律 谱元粘性法 收敛分析 |
| 修稿时间： | 2006-04-232006-10-29 |
Spectral Element Viscosity Methods for Nonlinear Conservation Laws on the Semi-Infinite Interval |
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| Liang Jiang Chuanju Xu.Spectral Element Viscosity Methods for Nonlinear Conservation Laws onthe Semi-Infinite Interval[J].Numerical Mathematics A Journal of Chinese Universities English Series,2007,16(2):112-130. |
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| Authors: | Liang Jiang Chuanju Xu |
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| Abstract: | In this paper we propose a spectral element: vanishing viscosity (SEW) method for the conservation laws on the semi-infinite interval. By using a suitable mapping, the problem is first transformed into a modified conservation law in a bounded interval, then the well-known spectral vanishing viscosity technique is generalized to the multi-domain case in order to approximate this trarsformed equation more efficiently. The construction details and convergence analysis are presented. Under a usual assumption of boundedness of the approximation solutions, it is proven that the solution of the SEW approximation converges to the uniciue entropy solution of the conservation laws. A number of numerical tests is carried out to confirm the theoretical results. |
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| Keywords: | Spectral element methods spectral vanishing viscosity conservation laws unbounded domain |
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