Anisotropic Rectangular Nonconforming Finite Element Analysis for Sobolev Equations

SHI Dong-yang; WANG Hai-hong; GUO Cheng

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SHI Dong-yang, WANG Hai-hong, GUO Cheng. Anisotropic Rectangular Nonconforming Finite Element Analysis for Sobolev Equations[J]. Applied Mathematics and Mechanics, 2008, 29(9): 1089-1100.

Citation:

SHI Dong-yang, WANG Hai-hong, GUO Cheng. Anisotropic Rectangular Nonconforming Finite Element Analysis for Sobolev Equations[J]. Applied Mathematics and Mechanics, 2008, 29(9): 1089-1100.

Citation:

SHI Dong-yang, WANG Hai-hong, GUO Cheng. Anisotropic Rectangular Nonconforming Finite Element Analysis for Sobolev Equations[J]. Applied Mathematics and Mechanics, 2008, 29(9): 1089-1100.

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Anisotropic Rectangular Nonconforming Finite Element Analysis for Sobolev Equations

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

Received Date: 2008-01-18
Rev Recd Date: 2008-08-01
Publish Date: 2008-09-15

Abstract

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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References(14)

References

[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
[2]	Nakao M T.Error estimate of a Galerkin method for some nonlinear Sobolev equations in one space dimension[J].Numer Math,1985,47(1):139-157. doi: 10.1007/BF01389881
[3]	JIANG Zi-wen, CHEN Huan-zhen.Error estimates of mixed finite element methods for sobolevequation[J].Northeast Math,2001,17(3):301-314.
[4]	郭玲,陈焕贞.Sobolev方程的H1-Galerkin混合有限元方法[J].系统科学与数学,2006,26(3):301-314.
[5]	Ciarlet P G. The Finite Element Method for Elliptic Problems[M].Amsterdam: North-Holland, 1978.
[6]	SHI Dong-yang,MAO Shi-peng, CHEN Shao-chun. An anisotropic nonconforming finiteelement with some superconvergence results[J].J Comput Math,2005,23(3):261-274.
[7]	LIN Qun,Tobiska L, ZHOU Ai-hui. Superconvergence and extrapolation of nonconforming low order finite elements applied to the Poisson equation[J].IMA J Numer Anal,2005,25(1):160-181. doi: 10.1093/imanum/drh008
[8]	Hale J K.Ordinary Differential Equations[M].New York:Willey-Inter Science,1969.
[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.
[11]	Heywood J G, Rannacher R. Finite element approximation of the nonstationary Navier-Stokes problem IV: Error analysis forsecond-order time discretization[J].SIAM J Numer Anal,1990,27(2):353-384. doi: 10.1137/0727022
[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
[13]	HE Yin-nian, SUN Wei-wei. Stability and convergence of the Crank-Nicolson/Adams-Bashforth scheme for the time-dependent Navier-Stokes equations[J].SIAM J Numer Anal,2007,45(2):837-869. doi: 10.1137/050639910
[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