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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 523909, 10 pages
http://dx.doi.org/10.1155/2013/523909
Research Article

Local Projection-Based Stabilized Mixed Finite Element Methods for Kirchhoff Plate Bending Problems

College of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, China

Received 5 December 2012; Accepted 18 February 2013

Academic Editor: Carlos Vazquez

Copyright © 2013 Xuehai Huang. 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.

Abstract

Based on stress-deflection variational formulation, we propose a family of local projection-based stabilized mixed finite element methods for Kirchhoff plate bending problems. According to the error equations, we obtain the error estimates of the approximation to stress tensor in energy norm. And by duality argument, error estimates of the approximation to deflection in H1-norm are achieved. Then we design an a posteriori error estimator which is closely related to the equilibrium equation, constitutive equation, and nonconformity of the finite element spaces. With the help of Zienkiewicz-Guzmán-Neilan element spaces, we prove the reliability of the a posteriori error estimator. And the efficiency of the a posteriori error estimator is proved by standard bubble function argument.