Nonconforming rotated Q_1 element on non-tensor product anisotropic meshes

作     者：MAO Shipeng SHI Zhongci 

作者机构：Institute of Computational Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences PO Box 2719 Beijing 100080 China Institute of Computational Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences PO Box 2719 Beijing 100080 China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2006年第49卷第10期

页      面：1363-1375页

核心收录：

学科分类：07[理学] 08[工学] 0701[理学-数学] 

基　　金：National Key Research and Development Program of China NKRDPC: 2005CB321701 

主　　题：anisotropic, interpolation error, consistency error, nonconforming rotated Q1 element. 

摘      要：In this paper, we consider the nonconforming rotated Q1 element for the second order elliptic problem on the non-tensor product anisotropic meshes, i.e. the anisotropic affine quadrilateral meshes. Though the interpolation error is divergent on the anisotropic meshes,we overcome this difficulty by constructing another proper operator. Then we give the optimal approximation error and the consistency error estimates under the anisotropic affine quadrilateral meshes. The results of this paper provide some hints to derive the anisotropic error of some finite elements whose interpolations do not satisfy the anisotropic interpolation properties. Lastly, a numerical test is carried out, which coincides with our theoretical analysis.