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

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• 作者：XiangYun Meng ; XueQin Yang ; Shuo Zhang
• 关键词：d ; rectangular Morley element ; second order elliptic equation ; convergence analysis ; super convergence ; lower bound estimate
• 刊名：SCIENCE CHINA Mathematics
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：59
• 期：11
• 页码：2245-2264
• 全文大小：434 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Chinese Library of Science
  Applications of Mathematics
  
• 出版者：Science China Press, co-published with Springer
• ISSN：1869-1862
• 卷排序：59

文摘

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(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.