各向异性网格下Wilson元的超收敛性分析

基金项目: 国家自然科学基金资助项目(10371113)

Superconvergence Analysis of Wilson’s Element on Anisotropic Meshes

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

摘要: 在各向异性网格下研究了二阶椭圆边值问题的Wilson有限元方法，利用单元构造的特殊性和一些新的技巧得到相应的超逼近和超收敛结果．数值算例的结果与理论分析是相吻合的．
- 各向异性网格 /
- Wilson元 /
- 超逼近 /
- 超收敛
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

[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.