| Sobolev方程的一类各向异性非协调有限元逼近 |
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| 引用本文： | 石东洋,谢萍丽.Sobolev方程的一类各向异性非协调有限元逼近[J].系统科学与数学,2009,29(1):116-128. |
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| 作者姓名： | 石东洋 谢萍丽 |
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| 作者单位： | 1. 郑州大学数学系,郑州,450052
2. 郑州大学数学系,郑州,450052;复旦大学数学科学学院,上海,200433 |
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| 摘 要： | 在各向异性网格下,分别讨论了Sobolev方程在半离散和全离散格式下的一类非协调有限元逼近,得到了与传统有限元方法相同的误差估计和一些超逼近性质.同时在半离散格式下,通过构造具有各向异性特征的插值后处理算子得到了整体超收敛结果.
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| 关 键 词： | Sobolev方程 各向异性网格 非协调有限元 后处理技术 超逼近和超收敛 |
| 收稿时间： | 2006-6-1 |
| 修稿时间： | 2007-11-9 |
A Kind of Nonconforming Finite Element Approximation to Sobolev Equations on Anisotropic Meshes |
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| SHI Dongyang,XIE Pingli.A Kind of Nonconforming Finite Element Approximation to Sobolev Equations on Anisotropic Meshes[J].Journal of Systems Science and Mathematical Sciences,2009,29(1):116-128. |
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| Authors: | SHI Dongyang XIE Pingli |
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| Institution: | (1)Department of Mathematics, Zhengzhou University, Zhengzhou 450052; (2)Department of Mathematics, Zhengzhou University, Zhengzhou 450052; School of Mathematical Sciences, Fudan University, Shanghai 200433. |
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| Abstract: | A kind of nonconforming finite element approximation to Sobolev equations is discussed with semidiscretization and full discretization on anisotropic meshes,respectively. The same optimal error estimates and superclose properties as the traditional finite element methods are derived. Furthermore, for the semidiscretization method, the global superconvergence is obtained through constructing an anisotropic post-processing operator. |
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| Keywords: | Sobolev equations anisotropic meshes nonconforming finite element post-processing technique superclose property and superconvergence |
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