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

• Published in: Science China. Mathematics Vol. 59; no. 11; pp. 2245 - 2264
• Main Authors: Meng, XiangYun, Yang, XueQin, Zhang, Shuo
• Format: Journal Article
• Language: English
• Published: Beijing Science China Press 01.11.2016; Springer Nature B.V
• Subjects: analysis;super; Applications of Mathematics; Automobile customizing; bound; Convergence; convergence;lower; d-rectangular; element;second; elliptic; equation;convergence; estimate; Mathematical models; Mathematics; Mathematics and Statistics; Morley; Norms; order; Triangulation; second order elliptic equation; lower bound estimate; rectangular Morley element; convergence analysis; super convergence; 65N22; 65N30
• ISSN: 1674-7283; 1869-1862
• DOI: 10.1007/s11425-015-0471-2

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.