| 非线性色散耗散波动方程的 Hermite型有限元分析(英文) |
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| 引用本文： | 樊明智,张建军,石东洋.非线性色散耗散波动方程的 Hermite型有限元分析(英文)[J].应用数学,2012,25(2):341-349. |
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| 作者姓名： | 樊明智 张建军 石东洋 |
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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. 郑州大学数学系,河南郑州,450001 |
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| 基金项目： | The NSF of China，The Tianyuan Mathematics Foundation of NSF of China，The NSF of the Education Department of Henan Province |
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| 摘 要： | 在半离散和全离散格式下对一类非线性色散耗散波动方程给出了 Hermite型有限元方法.利用已有高精度结果和插值后处理技巧,分别导出了超逼近和整体超收敛,通过构造新的辅助问题,得到了四阶精度的外推解.
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| 关 键 词： | 非线性色散耗散波动方程 Hermite有限元 超收敛和外推 半离散和全离散格式 |
Hermite-type Finite Element Analysis for Nonlinear Dispersion-dissipative Wave Equations |
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| FAN Mingzhi
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ZHANG Jianjun
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SHI Dongyang.Hermite-type Finite Element Analysis for Nonlinear Dispersion-dissipative Wave Equations[J].Mathematica Applicata,2012,25(2):341-349. |
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| Authors: | FAN Mingzhi ZHANG Jianjun SHI Dongyang |
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| Institution: | 1.School of Mathematics and Statistics,Xuchang University,Xuchang 461000,China;2.Department of Mathematics,Zhengzhou University,Zhengzhou 450001,China) |
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| Abstract: | An Hermite-type finite element method is proposed for a class of nonlinear dispersion-dissipative wave equations under semi-discrete and fully-discrete schemes.Based on the known high accurary result and interpolation post-processing technique,the superclose and global superconvergence are derived,respectively.Besides,the fourth-order extrapolation solution is deduced through constructing a new suitable auxiliary problem. |
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| Keywords: | Nonlinear dispersion-dissipative wave equation Hermite-type tinite element Superconvergence and extrapolation Semi-discrete and fully-discrete scheme |
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