Convergence of an Adaptive Finite Element Method for 2D Elasticity Problems

LIU Chun-mei; ZHONG Liu-qiang; SHU Shi; XIAO Ying-xiong

doi:10.3879/j.issn.1000-0887.2014.09.003

Volume 35 Issue 9

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Article Navigation > Applied Mathematics and Mechanics > 2014 > 35(9): 969-978

LIU Chun-mei, ZHONG Liu-qiang, SHU Shi, XIAO Ying-xiong. Convergence of an Adaptive Finite Element Method for 2D Elasticity Problems[J]. Applied Mathematics and Mechanics, 2014, 35(9): 969-978. doi: 10.3879/j.issn.1000-0887.2014.09.003

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Convergence of an Adaptive Finite Element Method for 2D Elasticity Problems

doi: 10.3879/j.issn.1000-0887.2014.09.003

¹Institute of Computational Mathematics, Department of Mathematical Sciences, Hunan University of Science and Engineering, Yongzhou, Hunan 425199, P.R.China;²School of Mathematical Sciences, South China Normal University, Guangzhou 510631, P.R.China;³School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan 411105, P.R.China;⁴College of Civil Engineering and Mechanics, Xiangtan University, Xiangtan, Hunan 411105, P.R.China

Funds: The National Natural Science Foundation of China(11201159)

Received Date: 2014-01-20
Publish Date: 2014-09-15

Abstract

Abstract

For 2D linear elasticity problems, firstly, a standard adaptive finite element method (AFEM) was developed based on the newest vertex bisection grid refinement, which was marked only according to the error estimators without special treatment of the oscillation terms and intended conformance to the interior node properties. Secondly, through analysis of the numerical solution functions and error indicators at all the grid levels, the AFEM was strictly proved to be convergent by means of the orthogonality between the numerical solution functions at adjacent grid levels, the upper bound estimation of the energy errors between the true solution functions and the numerical solution functions, and the approximate compressibility of the error indicators between adjacent grid levels. Finally, several numerical experiments confirm that the presented AFEM is convergent and robust.
- 2D elasticity problem,
- adaptive finite element method,
- convergence

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References

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