| Sobolev型方程各向异性网格下Wilson元的高精度分析 |
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| 引用本文： | 石东洋,任金城,郝晓斌.Sobolev型方程各向异性网格下Wilson元的高精度分析[J].高等学校计算数学学报,2009,31(2). |
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| 作者姓名： | 石东洋 任金城 郝晓斌 |
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| 作者单位： | 1. 郑州大学数学系,郑州,450052
2. 商丘师范学院数学系,商丘,476000 |
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| 基金项目： | 国家自然科学基金，河南省高等学校创新人才培养工程基金 |
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| 摘 要： | 1引言 Sobolev方程在流体穿过裂缝岩石的渗透理论,土壤中湿气的转移问题,不同介质的热传导问题等许多物理问题中都有广泛的应用,因此已有许多文献研究此方程2,6,8,9,11]但这些研究都是基于对剖分的正则性条件或拟一致假设7],即满足hk/pK≤C或h/h≤C,vK∈Th,其中hk,PK分别是一般单元K的最大直径和最大内切圆直径,h=maxhk,h=minhk,C是一个与h无关的正常数.
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| 关 键 词： | 方程 各向异性网格 精度分析 正则性 插值后处理 整体超收敛 多项式空间 拟一致 后验误差估计 |
HIGHER ACCURACY ANALYSIS FOR THE WILSON ELEMENT TO SOBOLEV TYPE EQUATION ON ANISOTROPIC MESHES |
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| Shi Dongyang,Ren Jincheng,Hao Xiaobin.HIGHER ACCURACY ANALYSIS FOR THE WILSON ELEMENT TO SOBOLEV TYPE EQUATION ON ANISOTROPIC MESHES[J].Numerical Mathematics A Journal of Chinese Universities,2009,31(2). |
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| Authors: | Shi Dongyang Ren Jincheng Hao Xiaobin |
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| Institution: | Shi Dongyang (Department of Mathematics,Zhengzhou University,Zhengzhou 450052) Ren Jincheng (Department of Mathematics,Shangqiu Normal University,Shangqiu 476000) Hao Xiaobin (Department of Mathematics,Zhengzhou 450052) |
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| Abstract: | In this paper,higher accuracy analysis of the Wilson element to Sobolev equation is discussed under anisotropic meshes.The superclose property, which is as the same as results on regular meshes are derived.Then,the superconvergence is obtained through the interpolation postproeessing technique.Two order higher convergence rate than general error estimate in H~1-norm is derived by use of extrapolation. |
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| Keywords: | Sobolev type equation anisotropic meshes higher accuracy postprocessing technique extrapolation |
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