American Institute of Mathematical Sciences

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January  2008, 9(1): 163-182. doi: 10.3934/dcdsb.2008.9.163

The patch recovery for finite element approximation of elasticity problems under quadrilateral meshes

Zhong-Ci Shi 1, , Xuejun Xu 1, and  Zhimin Zhang 2,

1. 

LSEC, Institute of Computational Mathematics, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100080, China, China
2. 

College of Mathematics and Computer Science, Hunan Normal University, Changsha, Hunan 410081, China

Received  January 2007 Revised  September 2007 Published  October 2007

In this paper, some patch recovery methods are proposed and analyzed for finite element approximation of elasticity problems using quadrilateral meshes. Under a mild mesh condition, superconvergence results are established for the recovered stress tensors. Consequently, a posteriori error estimators based on the recovered stress tensors are asymptotically exact.
Keywords: Finite element, Superconvergence, Gradient recovery, Linear elasticity..
Mathematics Subject Classification: Primary: 65N30. 65N15; Secondary: 65N12, 65D10, 41A1.
Citation: Zhong-Ci Shi, Xuejun Xu, Zhimin Zhang. The patch recovery for finite element approximation of elasticity problems under quadrilateral meshes. Discrete and Continuous Dynamical Systems - B, 2008, 9 (1) : 163-182. doi: 10.3934/dcdsb.2008.9.163
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