| 非线性双曲方程Hermite型矩形元的高精度分析 |
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| 引用本文： | 王芬玲,石东伟.非线性双曲方程Hermite型矩形元的高精度分析[J].山东大学学报(理学版),2012,47(10):89-96. |
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| 作者姓名： | 王芬玲 石东伟 |
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| 作者单位： | 1. 许昌学院数学与统计学院, 河南 许昌 461000; 2. 河南科技学院数学系, 河南 新乡 453000 |
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| 基金项目： | 国家自然科学基金资助项目，河南省科技厅项目基金资助项目，河南省教育厅自然科学基金资助项目 |
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| 摘 要： | 讨论了非线性双曲方程的Hermite型矩形有限元逼近。 利用该元的高精度分析、平均值理论和导数转移技巧得到了H1模意义下的超逼近性。 借助于插值后处理方法导出超收敛结果。最后,通过构造一个新的外推格式, 给出了与线性问题相同的四阶外推估计。
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| 关 键 词： | 非线性双曲方程 超逼近和超收敛 Hermite型矩形元 外推 |
| 收稿时间： | 2012-05-02 |
High analysis of Hermite-type rectangular element for nonlinear hyperbolic equation |
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| WANG Fen-ling,SHI Dong-wei.High analysis of Hermite-type rectangular element for nonlinear hyperbolic equation[J].Journal of Shandong University,2012,47(10):89-96. |
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| Authors: | WANG Fen-ling SHI Dong-wei |
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| Institution: | 1. School of Mathematics and Statistics, Xuchang University, Xuchang 461000, Henan, China;
2. Department of Mathematics, Henan Institute of Science and Technology, Xinxiang 453000, Henan, China |
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| Abstract: | A Hermite-type rectangular finite element approximation is discussed for nonlinear hyperbolic equation. The superclose property in H1-norm is obtained by use of high accuracy analysis of the element, mean value theorem and the derivative transfering technique. The superconvergence result is derived with interpolation postprocessing method. Finally, the fourth order extrapolation estimation which is as same as that of the linear problem is deduced through constructing a new extrapolation scheme. |
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| Keywords: | nonlinear hyperbolic equation superclose and superconvergence Hermite-type rectangular element ex- trapolation |
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