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Abstract and Applied Analysis
Volume 2014, Article ID 234375, 11 pages
Research Article

Convergence Analysis of Incomplete Biquadratic Rectangular Element for Fourth-Order Singular Perturbation Problem on Anisotropic Meshes

1School of Sciences, Henan University of Technology, Zhengzhou 450001, China
2School of Mathematics and Statistics, Anyang Normal University, Anyang 455000, China

Received 2 June 2013; Accepted 29 December 2013; Published 13 February 2014

Academic Editor: Youyu Wang

Copyright © 2014 Pingli Xie and Meng Hu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The convergence analysis of a Morley type rectangular element for the fourth-order elliptic singular perturbation problem is considered. A counterexample is provided to show that the element is not uniformly convergent with respect to the perturbation parameter. A modified finite element approximation scheme is used to get convergent results; the corresponding error estimate is presented under anisotropic meshes. Numerical experiments are also carried out to demonstrate the theoretical analysis.