| Sobolev型方程各向异性Carey元解的高精度分析 |
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| 引用本文： | 石东洋,郝晓斌.Sobolev型方程各向异性Carey元解的高精度分析[J].工程数学学报,2009,26(6). |
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| 作者姓名： | 石东洋 郝晓斌 |
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| 作者单位： | 石东洋(郑州大学数学系,郑州,450052);郝晓斌(河南工程学院数理科学系,郑州,451191) |
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| 基金项目： | 国家自然科学基金，河南工程学院博士基金 |
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| 摘 要： | 利用积分恒等式和插值后处理技术,本文在各向异性网格上对Sobolev型方程的Carey非协调有限元解进行高精度算法分析.首先,根据Carey元的特性,即其有限元解的线性插值和线性元解相同,我们构造插值后处理算子,得到了有限元解的超逼近性质和整体超收敛及后验误差估计.接着,根据误差渐近展开式,运用外推方法,进一步得到了具有四阶精度的近似解.
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| 关 键 词： | Sobolev型方程 Carey元 高精度分析 |
Higher Accuracy Analysis for the Anisotropic Carey Element Solution to Sobolev Type Equation |
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| SHI Dong-yang,HAO Xiao-bin.Higher Accuracy Analysis for the Anisotropic Carey Element Solution to Sobolev Type Equation[J].Chinese Journal of Engineering Mathematics,2009,26(6). |
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| Authors: | SHI Dong-yang HAO Xiao-bin |
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| Affiliation: | SHI Dong-yang1,HAO Xiao-bin2(1-Department of Mathematics,Zhengzhou University,Zhengzhou 450052,2-Department of Mathematical and Physical Sciences,Henan Institute of Engineering,Zhengzhou 451191) |
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| Abstract: | By using the integral identities and the interpolation postprocessing technique, the higher accuracy approximation of the anisotropic nonconforming Carey element for solving the Sobolev type equations is investigated. Firstly, the interpolation operator is constructed, the superclose, global superconvergence and posteriori error estimate are obtained with the help of the distinct property of Carey elements, i.e., the linear interpolation of the solution for Carey elements is equal to the solution for linear triangular element. Secondly, by virtue of the extrapolation method, the accuracy of the related approximate solution with fourth order is derived through the asymptotic error expansion. |
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| Keywords: | Sobolev type equations Carey element higher accuracy |
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