Superconvergence Analysis of Wilson’s Element on Anisotropic Meshes

SHI Dong-yang; LIANG Hui

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2007 > 28(1): 107-113

SHI Dong-yang, LIANG Hui. Superconvergence Analysis of Wilson’s Element on Anisotropic Meshes[J]. Applied Mathematics and Mechanics, 2007, 28(1): 107-113.

Citation:

SHI Dong-yang, LIANG Hui. Superconvergence Analysis of Wilson’s Element on Anisotropic Meshes[J]. Applied Mathematics and Mechanics, 2007, 28(1): 107-113.

Citation:

SHI Dong-yang, LIANG Hui. Superconvergence Analysis of Wilson’s Element on Anisotropic Meshes[J]. Applied Mathematics and Mechanics, 2007, 28(1): 107-113.

PDF( 296 KB)

Superconvergence Analysis of Wilson’s Element on Anisotropic Meshes

SHI Dong-yang¹,
LIANG Hui²

1.
Department of Mathematics, Zhengzhou University, Zhengzhou, 450052, P. R. China;

Received Date: 2005-03-01
Rev Recd Date: 2006-09-18
Publish Date: 2007-01-15

Abstract

Abstract

The Wilson finite element method is considered to solve a class of two-dimensional second order elliptic boundary value problems. By using the particular structure of the element and some new techniques, the superclose and global superconvergence on anisotropic meshes are obtained. Numerical example is also given to confirm our theoretical analysis.
- anisotropic meshes,
- Wilson's element,
- superclose,
- superconvergence

FullText(HTML)

References(9)

References

[1]	Ciarlet P G.The Finite Element Method for Elliptic Problem[M].Amsterdam:North-Holland,1978.
[2]	Shi Z C,Jiang B,Xue W M.A new superconvergence property of Wilson nonconforming finite element[J].Numer Math,1997,78(2):259-268. doi: 10.1007/s002110050312
[3]	Luo P,Lin Q.High accuracy analysis of the Wilson element[J].J of Comp Math,1999,17(2):113-124.
[4]	林群，严宁宁.高效有限元构造与分析[M].石家庄：河北大学出版社，1996.
[5]	石东洋，陈绍春.一类改进的Wilson任意四边形单元[J].高等学校计算数学学报，1994,16(2):161-167.
[6]	Chen S C,Zhao Y C,Shi D Y.Anisotropic interpolation with application to nonconforming elements[J].Appl Numer Math,2004,49(2):135-152. doi: 10.1016/j.apnum.2003.07.005
[7]	Zienissek A,Vanmaele M.The interpolation theorem for narrow quadrilateral isotropic metric finite elements[J].Numer Math,1995,72(1):123-141. doi: 10.1007/s002110050163
[8]	Apel Th,Dobrowolski M.Anisotropic interpolation with applications to the finite element method[J].Computing,1992,47(3):277-293. doi: 10.1007/BF02320197
[9]	Apel Th.Anisotropic Finite Elements:Local Estimate and Applications[M].Stuttgart，Leipzig:B G Teubner,1999.