Sobolev方程各向异性矩形非协调有限元分析

石东洋; 王海红; 郭城

Sobolev方程各向异性矩形非协调有限元分析

郑州大学数学系,郑州 450052

基金项目: 国家自然科学基金资助项目(10671184)

详细信息

作者简介:
石东洋(1961- ),男,河南鲁山人,博士(联系人.Tel:+86-371-67767813;E-mail:shi-dy@zzu.edu.cn).

中图分类号: O242.21
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出版历程
- 收稿日期: 2008-01-18
- 修回日期: 2008-08-01
- 刊出日期: 2008-09-15

Anisotropic Rectangular Nonconforming Finite Element Analysis for Sobolev Equations

Department of Mathematics, Zhengzhou University, Zhengzhou 450052, P. R. China

摘要

摘要: 研究了Sobolev方程的各向异性矩形非协调有限元方法．在半离散和全离散格式下,得到了与传统协调有限元方法相同的最优误差估计和超逼近性质．进一步地利用插值后处理技术得到了整体超收敛结果．最后的数值结果表明了理论分析的正确性．
- 非协调元 /
- 各向异性 /
- Sobolev方程 /
- 误差估计 /
- 超收敛
Abstract: The anisotropic rectangular nonconforming finite element method to Sobolev equations is discussed under semi-discrete and full discrete schemes, the corresponding optimal convergence error estimates and superclose property are derived, which are the same as the traditional conforming finite elements. Furthermore, the global superconvergence is obtained through post-processing technique. Finally, the numerical results illustrate the validity of our theoretical analysis.
- nonconforming element /
- anisotropy /
- Sobolev equations /
- error estimates /
- superconvergence

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参考文献(14)

[1]	Ewing R E.Time-stepping Galerkin methods for nonlinear Sobolev partial-differential equations[J].SIAM J Numer Anal,1978,15(6):1125-1150. doi: 10.1137/0715075
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[9]	石东洋,谢萍丽,陈绍春.双曲积分微分方程的各向异性非协调有限元逼近[J].应用数学学报,2007,30(4):654-666.
[10]	林群,严宁宁.高效有限元构造与分析[M].保定: 河北大学出版社,1996.
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[12]	HE Yin-nian. Two-level method based on finite element and Crank-Nicolson extrapolation for time-dependent Navier-Stokes equations[J].SIAM J Numer Anal,2003,41(4):1263-1283. doi: 10.1137/S0036142901385659
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[14]	HE Yin-nian, SUN Wei-wei. Stabilized finite element methods based on Crank-Nicolson extrapolation scheme for the time-dependent Navier-Stokes equations[J].Math Comp,2007,76(257):115-136. doi: 10.1090/S0025-5718-06-01886-2

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Sobolev方程各向异性矩形非协调有限元分析

作者简介:
石东洋(1961- ),男,河南鲁山人,博士(联系人.Tel:+86-371-67767813;E-mail:shi-dy@zzu.edu.cn).

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Anisotropic Rectangular Nonconforming Finite Element Analysis for Sobolev Equations

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留言板

Sobolev方程各向异性矩形非协调有限元分析

作者简介: 石东洋(1961- ),男,河南鲁山人,博士(联系人.Tel:+86-371-67767813;E-mail:shi-dy@zzu.edu.cn).

计量

出版历程

Anisotropic Rectangular Nonconforming Finite Element Analysis for Sobolev Equations

计量

出版历程

目录

作者简介:
石东洋(1961- ),男,河南鲁山人,博士(联系人.Tel:+86-371-67767813;E-mail:shi-dy@zzu.edu.cn).