| 非线性黏弹性方程双线性元解的高精度分析 |
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| 引用本文： | 牛裕琪,王芬玲,石东伟. 非线性黏弹性方程双线性元解的高精度分析[J]. 山东大学学报(理学版), 2011, 46(8): 31-37 |
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| 作者姓名： | 牛裕琪 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 453003 |
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| 基金项目： | 国家自然科学基金数学天元基金(11026154); 河南省教育厅自然科学基金资助项目(2010A110018;2011A110020) |
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| 摘 要： | 利用积分恒等式和平均值技巧,给出了非线性黏弹性方程的双线性元逼近,得到了H1模意义下的O(h2)阶超逼近性质。同时借助插值后处理技术,导出了整体超收敛结果。在此基础上, 通过构造合适的外推格式,得到了具有更高精度O(h3)阶的近似解。
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| 关 键 词： | 非线性黏弹性方程 双线性元 高精度分析 插值后处理 外推, |
| 收稿时间： | 2011-01-31 |
Higher accuracy analysis for the bilinear element solution of nonlinear viscoelasticity type equations |
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| NIU Yu-qi,WANG Fen-ling,SHI Dong-wei. Higher accuracy analysis for the bilinear element solution of nonlinear viscoelasticity type equations[J]. Journal of Shandong University, 2011, 46(8): 31-37 |
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| Authors: | NIU Yu-qi WANG Fen-ling SHI Dong-wei |
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| Affiliation: | 1. School of Mathematics and Statistics, Xuchang University, Xuchang 461000, Henan, China;
2. Department of Mathematics, Henan Insititute of Science and Technology, Xinxiang 453003, Henan, China |
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| Abstract: | In this paper,by use of the integral identities and the mean value technique,approximation of bilinear finite element for the nonlinear viscoelasticity type equations with superclose property of order O(h2) in H1-norm is obtained.A global super-convergence result is yielded by interpolated post-processing method.Then higher accuracy of order O(h3) for approximation solution are derived through constructing a proper extrapolation scheme. |
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| Keywords: | nonliear viscoelasticity type equations bilinear element higher accuracy interpolated post-processing extrapolation |
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