Convergence analysis of the rectangular Morley element scheme for second order problem in arbitrary dimensions  

作　　者：MENG XiangYun YANG XueQin ZHANG Shuo 

机构地区：[1]School of Mathematical Sciences, Peking University [2]LSEC, ICMSEC, NCMIS, Academy of Mathematics and Systems Science,Chinese Academy of Sciences

出　　处：《Science China Mathematics》2016年第11期2245-2264,共20页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 11471026, 11271035, 91430213, 11421101 and 11101415)

摘　　要：We present the convergence analysis of the rectangular Morley element scheme utilised on the second order problem in arbitrary dimensions. Specifically, we prove that the convergence of the scheme is of （D（h） order in energy norm and of O（h2） order in L2 norm on general d-rectangular triangulations. Moreover, when the triangulation is uniform, the convergence rate can be of O（h2） order in energy norm, and the convergence rate in L2 norm is still of O（h2） order, which cannot be improved. Numerical examples are presented to demonstrate our theoretical results.We present the convergence analysis of the rectangular Morley element scheme utilised on the second order problem in arbitrary dimensions. Specifically, we prove that the convergence of the scheme is of O(h) order in energy norm and of O(h^2) order in L^2 norm on general d-rectangular triangulations. Moreover, when the triangulation is uniform, the convergence rate can be of O(h^2) order in energy norm, and the convergence rate in L^2 norm is still of O(h^2) order, which cannot be improved. Numerical examples are presented to demonstrate our theoretical results.

关 键 词：d-rectangular Morley element second order elliptic equation convergence analysis super convergence lower bound estimate 

分 类 号：O175.25[理学—数学]